Source code for triqs_ctseg.solver
-from .solver_core import SolverCore
+# Copyright (c) 2022-2024 Simons Foundation
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You may obtain a copy of the License at
+# https:#www.gnu.org/licenses/gpl-3.0.txt
+#
+# Authors: Olivier Parcollet, nkavokine
+
+from .solver_core import SolverCore
from triqs.gf import *
from triqs.utility import mpi
diff --git a/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.D0_tau.html b/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.D0_tau.html
index 822769d19e..4c9eaf98be 100644
--- a/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.D0_tau.html
+++ b/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.D0_tau.html
@@ -88,9 +88,8 @@
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters diff --git a/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.Delta_tau.html b/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.Delta_tau.html index cd120aaae5..565ddef667 100644 --- a/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.Delta_tau.html +++ b/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.Delta_tau.html @@ -88,9 +88,8 @@
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters diff --git a/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.Jperp_tau.html b/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.Jperp_tau.html index 976d6c9bd6..5a789c7858 100644 --- a/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.Jperp_tau.html +++ b/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.Jperp_tau.html @@ -88,9 +88,8 @@
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters diff --git a/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.__init__.html b/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.__init__.html index 8b80c81d6d..c675a84038 100644 --- a/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.__init__.html +++ b/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.__init__.html @@ -86,9 +86,8 @@
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters @@ -234,7 +233,7 @@
- Step 2 - Construct the solver
- Step 3 - Supply the solver inputs
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters @@ -232,7 +231,7 @@
- Step 2 - Construct the solver
- Step 3 - Supply the solver inputs
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters diff --git a/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.results.html b/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.results.html index 640af8f499..09be061329 100644 --- a/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.results.html +++ b/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.results.html @@ -86,9 +86,8 @@
- Step 2 - Construct the solver
- Step 3 - Supply the solver inputs
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters diff --git a/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.solve.html b/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.solve.html index c63c54c495..1a24356d70 100644 --- a/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.solve.html +++ b/ctseg/3.3.x/_ref/triqs_ctseg.solver.Solver.solve.html @@ -17,8 +17,6 @@ - - @@ -88,9 +86,8 @@
- Step 2 - Construct the solver
- Step 3 - Supply the solver inputs
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters @@ -224,12 +221,22 @@
Parameters
h_int
triqs::operators::many_body_operator
–
Local Hamiltonian
Quartic part of the local Hamiltonian
- Step 2 - Construct the solver
- Step 3 - Supply the solver inputs
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters @@ -222,12 +219,22 @@
triqs_ctseg.solver.Solver.solve_params
h_int
triqs::operators::many_body_operator
–
Local Hamiltonian
Quartic part of the local Hamiltonian
- Step 2 - Construct the solver
- Step 3 - Supply the solver inputs
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters diff --git a/ctseg/3.3.x/algorithm_implementation/ctseg.html b/ctseg/3.3.x/algorithm_implementation/ctseg.html index e0398c3858..809fa648ff 100644 --- a/ctseg/3.3.x/algorithm_implementation/ctseg.html +++ b/ctseg/3.3.x/algorithm_implementation/ctseg.html @@ -88,9 +88,8 @@
- Step 2 - Construct the solver
- Step 3 - Supply the solver inputs
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters @@ -215,7 +214,7 @@
Double expansion \[\begin{split}\begin{split} \mathcal{S} &= \iint_0^{\beta} \mathrm{d} \tau \mathrm{d} \tau' \sum_{a,b} \left\{ \overline{c}_{a\sigma} (\tau) -\left( (\partial_{\tau} + \mu_{a\sigma})\delta_{ab}^{\sigma \sigma'} \delta_{\tau - \tau'} + \Delta_{ab}^{\sigma \sigma'}(\tau - \tau')\right) +\left( (\partial_{\tau} + \epsilon_{a\sigma} - \mu)\delta_{ab}^{\sigma \sigma'} \delta_{\tau - \tau'} + \Delta_{ab}^{\sigma \sigma'}(\tau - \tau')\right) c_{b\sigma'}(\tau') \right\} \\ &+ \frac{1}{2} \iint_0^{\beta} \mathrm{d} \tau \mathrm{d} \tau' \sum_{a,b} \mathcal{U}_{ab}(\tau - \tau') n_a(\tau) n_b(\tau') + \frac{1}{2} \iint_0^{\beta} \mathrm{d} \tau \mathrm{d} \tau' \sum_{a, \xi = x, y, z} s_a^{\xi}(\tau) \mathcal{J}_a^{\xi}(\tau - \tau') s_a^{\xi} (\tau') @@ -224,12 +223,13 @@
Double expansion\(n_a \equiv \sum_{\sigma} n_{a\sigma}\), \(s_a^{\xi} \equiv \frac{1}{2} \sum_{\sigma \sigma'} \overline{c}_{a\sigma} \sigma_{\sigma \sigma'}^{\xi} c_{a \sigma'}\) and \(\sigma^{\xi}\) are the Pauli matrices. \(\overline{c}_{a\sigma}(\tau)\) and \(c_{a\sigma}(\tau)\) are the \(\beta\)-antiperiodic Grassmann fields corresponding to the fermion -creation and annihilation operators on the impurity, respectively. +creation and annihilation operators on the impurity, respectively. The \(\epsilon_{a\sigma}\) are orbital energies and \(mu\) +is the chemical potential.
This action can be recast as
\[\begin{split}\begin{split} \mathcal{S} &= \iint_0^{\beta} \mathrm{d} \tau \mathrm{d} \tau' \sum_{a,b} \left\{ \overline{c}_{a\sigma} (\tau) -\left( (\partial_{\tau} + \mu_{a\sigma})\delta_{ab}^{\sigma \sigma'} \delta_{\tau - \tau'} + \Delta_{ab}^{\sigma \sigma'}(\tau - \tau')\right) +\left( (\partial_{\tau} + \epsilon_{a\sigma} - mu)\delta_{ab}^{\sigma \sigma'} \delta_{\tau - \tau'} + \Delta_{ab}^{\sigma \sigma'}(\tau - \tau')\right) c_{b\sigma'}(\tau') \right\} \\ &+ \frac{1}{2} \iint_0^{\beta} \mathrm{d} \tau \mathrm{d} \tau' \sum_{u,v} \mathcal{U}_{uv}(\tau - \tau') n_u(\tau) n_v(\tau') + \frac{1}{2} \iint_0^{\beta} \mathrm{d} \tau \mathrm{d} \tau' \sum_{a} \mathcal{J}_a^{\perp}(\tau - \tau') s_a^{+}(\tau) s_a^{-} (\tau') @@ -237,7 +237,7 @@-Double expansion \[\mathcal{U}_{uv}(\tau - \tau') = \mathcal{U}_{ab}(\tau - \tau') + (-1)^{\sigma \sigma'} \frac{1}{4} \mathcal{J}_a^z(\tau) \delta_{ab},\]
\(s^{\pm} = s_x \pm i s_y\) and \(\mathcal{J}^{\perp} \equiv \mathcal{J}^x = \mathcal{J}^y\). The CTSEG solver +
\(s^{\pm} = S_x \pm i s_y\) and \(\mathcal{J}^{\perp} \equiv \mathcal{J}^x = \mathcal{J}^y\). The CTSEG solver stochastically explores the terms (or configurations) generated by the expansion of \(\mathcal{S}\) in powers of \(\Delta(\tau)\) and \(\mathcal{J}^{\perp}(\tau)\) and samples the observables of interest (e.g. the Green’s function) every few configurations.
@@ -275,7 +275,7 @@Configuration\(O_{ab}\) is the overlap between the segments of colors \(a\) and \(b\), and \(\ell_a\) is the occupied length in color a. In the presence of dynamical interactions, the static trace factor is computed with a renormalized interaction and chemical potential: -\(\tilde U_{ab} = U_{ab} - 2 K'_{ab}(0)\) and \(\tilde \mu_{a} = \mu_a + K'_{aa}(0)\). +\(\tilde U_{ab} = U_{ab} - 2 K'_{ab}(0)\) and \(\tilde \mu_{a} = \mu - \epsilon_a + K'_{aa}(0)\).
Sign
diff --git a/ctseg/3.3.x/algorithm_implementation/implementation_notes.html b/ctseg/3.3.x/algorithm_implementation/implementation_notes.html index 37208e4551..7476bad9e0 100644 --- a/ctseg/3.3.x/algorithm_implementation/implementation_notes.html +++ b/ctseg/3.3.x/algorithm_implementation/implementation_notes.html @@ -88,9 +88,8 @@ - Step 2 - Construct the solver
- Step 3 - Supply the solver inputs
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters @@ -234,8 +233,8 @@
Inputs< The choice of the block structure is usually not unique, but using as many blocks as possible ensures the fastest determinant updates.
D0_tauis the dynamical part of the density-density interaction. Note that the static part is supplied in -thesolve_paramsas part of the interaction Hamiltonian. It should be supplied as a matrix-valuedGfImTime-(no block structure).
+the Jperp_tauis the perpendicular spin-spin interaction. It should be supplied as a \(1 \times 1\) matrix-valuedGfImTime.
diff --git a/ctseg/3.3.x/documentation.html b/ctseg/3.3.x/documentation.html
index e5fdf718ec..9b40199fc9 100644
--- a/ctseg/3.3.x/documentation.html
+++ b/ctseg/3.3.x/documentation.html
@@ -86,9 +86,8 @@
- Step 2 - Construct the solver
- Step 3 - Supply the solver inputs
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters diff --git a/ctseg/3.3.x/genindex.html b/ctseg/3.3.x/genindex.html index df40789048..0d221bdc42 100644 --- a/ctseg/3.3.x/genindex.html +++ b/ctseg/3.3.x/genindex.html @@ -83,9 +83,8 @@
- Step 2 - Construct the solver
- Step 3 - Supply the solver inputs
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters diff --git a/ctseg/3.3.x/guide/measurements.html b/ctseg/3.3.x/guide/measurements.html index 58c0ceb66e..129a945d8d 100644 --- a/ctseg/3.3.x/guide/measurements.html +++ b/ctseg/3.3.x/guide/measurements.html @@ -88,9 +88,8 @@
- Step 2 - Construct the solver
- Step 3 - Supply the solver inputs
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters @@ -215,13 +214,14 @@
Imaginary time Green’s function\(A\) is a block index and \(i, j\) are inner indices within the block. The block structure of \(G_{ij}^A(\tau)\) (valid values of the indices) is set by
gf_structin theconstr_params. -It is measured on a uniform time grid, whose number of points is set byn_tauin theconstr_params. +It is measured on a uniform time grid, whose number of points is set byn_tau_Gin thesolve_params+(defaults ton_tauinconstr_params).-Warning
The value of
n_tausupplied in theconstr_paramsand the number of points in the \(\tau\) grid of the \(\Delta(\tau)\) input must match.The measurement is turned on by setting
measure_gtin thesolve_paramstoTrue. The result of the +The measurement is turned on by setting
measure_G_tauin thesolve_paramstoTrue. The result of the accumulation is accessible through theresults.G_tauattribute of the solver object.@@ -248,54 +248,54 @@ Self-energy improved estimator \[\Sigma^A(i\omega_n) = [G^A]^{-1}(i\omega_n) F^A(i \omega_n).\]
The block structure and imaginary time grid for the improved estimator are the same as for the Green’s function. -The measurement is turned on by setting
measure_ftin thesolve_paramstoTrue. The result of the +The measurement is turned on by settingmeasure_F_tauin thesolve_paramstoTrue. The result of the accumulation is accessible through theresults.F_tauattribute of the solver object.Density
The average density is
-\[\langle n_i \rangle = \frac{1}{\beta} \int_0^{\beta} d \tau \langle n_i(\tau) \rangle.\]-Here the index \(i = 0, \dots N - 1\) represents the color (irrespective of the block structure). The measurement -is turned on by setting
+\[\langle n^A_i \rangle = \frac{1}{\beta} \int_0^{\beta} d \tau \langle n^A_i(\tau) \rangle.\] +measure_nin thesolve_paramstoTrue. The result of the -accumulation is accessible through theresults.densitiesattribute of the solver object, as a numpy -array of size \(N\).Here \(A\) represents a block name and \(i\) an index within the block. The measurement +is turned on by setting
measure_densitiesin thesolve_paramstoTrue. The result of the +accumulation is accessible through theresults.densitiesattribute of the solver object, as a Python +dictionary that associates a numpy vector to a block name. For example, the average density in the first +color of the spin up block is accessed asresults.densities["up"][0].Static density correlation function
The static density correlation function is defined as
-\[\langle n_i n_j \rangle = \frac{1}{\beta} \int_0^{\beta} d \tau \langle n_i(\tau) n_j(\tau) \rangle.\]-Here the indices \(i, j = 0, \dots N - 1\) represents colors (irrespective of the block structure). The measurement -is turned on by setting
+\[\langle n^A_i n^B_j \rangle = \frac{1}{\beta} \int_0^{\beta} d \tau \langle n^A_i(\tau) n^A_j(\tau) \rangle.\] +measure_nnin thesolve_paramstoTrue. The result of the -accumulation is accessible through theresults.nn_staticattribute of the solver object, as a numpy -array of size \(N \times N\).Here \(A, B\) represents block names and \(i, j\) indices within the block. The measurement +is turned on by setting
measure_nn_staticin thesolve_paramstoTrue. The result of the +accumulation is accessible through theresults.nn_staticattribute of the solver object, as a Python +dictionary that associates a matrix to a pair of block names. For example the static density correlation function +of the spin up block with itself is acccessed asresults.nn_static[("up", "up")].Dynamic density correlation function
The dynamic density correlation function is defined as
-\[\chi_{ij}(\tau) = \langle T_{\tau} n_i(\tau) n_j(0) \rangle.\]+\[\chi^{AB}_{ij}(\tau) = \langle T_{\tau} n^A_i(\tau) n^B_j(0) \rangle.\]Here the indices \(i, j = 0, \dots N - 1\) represents colors (irrespective of the block structure). -\(\chi_{ij}(\tau)\) is measured on a uniform time grid, whose number of points is set by
-n_tau_kin theconstr_params.--Warning
-The value of
-n_tau_ksupplied in theconstr_paramsand the number of points in the \(\tau\) grids of -the \(D(\tau)\) and \(J_{\perp}(\tau)\) inputs must match.The measurement is turned on by setting
+\(\chi_{ij}(\tau)\) is measured on a uniform time grid, whose number of points is set bymeasure_nntin thesolve_paramstoTrue. The result of the -accumulation is accessible through theresults.nn_tauattribute of the solver object, as a matrix-valued -GfImTimewith size \(N \times N\).n_tau_chi2in thesolve_params+(which defaults ton_tau_bosonicfromconstr_params). +The measurement is turned on by setting
measure_nn_tauin thesolve_paramstoTrue. The result of the +accumulation is accessible through theresults.nn_tauattribute of the solver object, as a +Block2Gf. For example, the correlation function in the first color of the spin up block is accessed as +results.nn_tau["up", "up"][0, 0].Perpendicular spin-spin correlation function
The perpendicular spin-spin correlation function is defined as
\[\chi^{\perp}(\tau) = \langle T_{\tau} s^x(\tau) s^x(0) \rangle.\]-\(\chi^{\perp}(\tau)\) is measured on a uniform time grid, whose number of points is set by
-n_tau_kin theconstr_params. -This measurement is useful if rotational invariance is broken (for instance, in the presence of a Zeeman field). Otherwise, -all components of the spin-spin correlation function can be determined from \(\chi_{ij}(\tau)\), with better statistics.The measurement is turned on by setting
measure_sperptin thesolve_paramstoTrue. The result of the +\(\chi^{\perp}(\tau)\) is measured on a uniform time grid, whose number of points is set by
+n_tau_chi2in thesolve_params+(which defaults ton_tau_bosonicfromconstr_params). +This measurement is useful if rotational invariance is broken (for instance, in the presence of a Zeeman field). It is +implemented for a single orbital only. Otherwise, all components of the spin-spin correlation function can be determined from \(\chi_{ij}(\tau)\), with better statistics.The measurement is turned on by setting
measure_sperp_tauin thesolve_paramstoTrue. The result of the accumulation is accessible through theresults.sperp_tauattribute of the solver object, as a matrix-valuedGfImTimewith size \(1 \times 1\).State histogram\(|00\rangle, |10\rangle, |01 \rangle, |11\rangle\). -
The measurement is turned on by setting
measure_statehistin thesolve_paramstoTrue. The result of the +The measurement is turned on by setting
measure_state_histin thesolve_paramstoTrue. The result of the accumulation is accessible through theresults.state_histattribute of the solver object, as a numpy array of size \(2^N\). The index of the state \(|n_0, n_1, \dots n_N \rangle\) in the histogram is given by \(\sum_{i = 0}^{N - 1} n_i 2^i\).Average sign
This measurement computes the average sign of the weight of the configuration. -The measurement is turned on by setting
+It is always on. The result of the accumulation is accessible through themeasure_signin thesolve_paramstoTrue. The result of the -accumulation is accessible through theresults.signattribute of the solver object as a double precision scalar.results.average_sign+attribute of the solver object as a double precision scalar.Perturbation order histograms
This measurement determines the histograms of the perturbation orders in \(\Delta(\tau)\) and \(\mathcal{J}_{\perp}(\tau)\). -The measurement is turned on by setting
+The measurement is turned on by settingmeasure_statehistin thesolve_paramstoTrue. The results of the -accumulation are accessible through theresults.perturbation_order_histo_Deltaandresults.perturbation_order_histo_Jperp-attributes of the solver, as TRIQS histogram objects.measure_pert_orderin thesolve_paramstoTrue. The results of the +accumulation are accessible through theresults.pert_order_Deltaandresults.pert_order_Jperp+attributes of the solver, as TRIQS histogram objects. The average orders can also be directly accessed via +results.average_order_Deltaandresults.average_order_Jperp. - Step 2 - Construct the solver
- Step 3 - Supply the solver inputs
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters diff --git a/ctseg/3.3.x/guide/step_by_step.html b/ctseg/3.3.x/guide/step_by_step.html index e54eddddd1..406b5c9567 100644 --- a/ctseg/3.3.x/guide/step_by_step.html +++ b/ctseg/3.3.x/guide/step_by_step.html @@ -88,9 +88,8 @@
- Step 2 - Construct the solver
- Step 3 - Supply the solver inputs
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters @@ -214,15 +213,23 @@
gf_structspecifies the block structure of the impurity Green’s function (see below).betais the inverse temperature.
-n_tauis the number of points of the imaginary time grid on which the fermionic two-point functions (input hybridization \(\Delta(\tau)\), measured Green’s function \(G(\tau)\), etc.) will be sampled.
-n_tau_kis the number of points of the imaginary time grid on which the bosonic two-point functions (input dynamical intercation \(D_0(\tau)\), measured density correlation function \(\chi(\tau)\), etc.) will be sampled.
+-
+
n_tauis the number of points of the imaginary time grid on which the input hybridization \(\Delta(\tau)\) is sampled.It is also the default number of samples for the measured fermionic two-point functions.
+
+
+-
+
n_tau_bosonicis the number of points of the imaginary time grid on which the bosonic two-point function inputs (\(D_0(\tau)\) and \(\mathcal{J}_{\perp}(\tau)\)) are sampled.It is also the default number of samples for the measured bosonic two-point functions.
+
+
h_intis the local interaction Hamiltonian (see above).
-chemical_potentialis the total orbital-dependent chemical potential (see above).
+h_loc0is quadratic part of the local Hamiltonian (see above).length_cycleis the length of a Monte Carlo cycle. Observables are sampled everylength_cycleMonte Carlo moves (either accepted or rejected).n_warmup_cyclesis the number of cycles to do before any observables are samples, so as to “forget” the initial configuration.n_cyclesis the number of cycles used for the production run.
@@ -432,9 +456,11 @@ Measure control. All the measurements can be switched on and off. Some of the measurements (self-energy improved estimator, density correlation functions) can be time-consuming, and they are off by default. For example, to turn the improved estimator -measurement on, one should set
solve_params["measure_ft"] = True.
+measurement on, one should set Move control. All the Monte Carlo moves can be switched on and off. This functionality exists to facilitate testing for developers. The solver chooses the relevant moves depending on its inputs, and regular users should not need move control.
+Optional sample numbers for the measured two-point functions:
n_tau_G(defaults ton_tau) for fermionic functions +andn_tau_chi2(defaults ton_tau_bosonic) for bosonic functions.- Step 2 - Construct the solver
- Step 3 - Supply the solver inputs
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters @@ -212,7 +211,7 @@
- Step 2 - Construct the solver
- Step 3 - Supply the solver inputs
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters diff --git a/ctseg/3.3.x/issues.html b/ctseg/3.3.x/issues.html index ab5cfa401e..a72bc8c996 100644 --- a/ctseg/3.3.x/issues.html +++ b/ctseg/3.3.x/issues.html @@ -86,9 +86,8 @@
- Step 2 - Construct the solver
- Step 3 - Supply the solver inputs
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters diff --git a/ctseg/3.3.x/search.html b/ctseg/3.3.x/search.html index 6197df02ec..25a6bd9dbb 100644 --- a/ctseg/3.3.x/search.html +++ b/ctseg/3.3.x/search.html @@ -86,9 +86,8 @@
- Step 2 - Construct the solver
- Step 3 - Supply the solver inputs
-
-
- Interaction Hamiltonian +
- Local Hamiltonian
- Hybridization function -
- Chemical potential
- Dynamical density-density interaction
- Spin-spin interaction
- Solve parameters diff --git a/ctseg/3.3.x/searchindex.js b/ctseg/3.3.x/searchindex.js index 41cca4fc89..582dad428d 100644 --- a/ctseg/3.3.x/searchindex.js +++ b/ctseg/3.3.x/searchindex.js @@ -1 +1 @@ -Search.setIndex({"docnames": ["ChangeLog", "_ref/triqs_ctseg.solver.Solver", "_ref/triqs_ctseg.solver.Solver.D0_tau", "_ref/triqs_ctseg.solver.Solver.Delta_tau", "_ref/triqs_ctseg.solver.Solver.Jperp_tau", "_ref/triqs_ctseg.solver.Solver.__init__", "_ref/triqs_ctseg.solver.Solver.constr_params", "_ref/triqs_ctseg.solver.Solver.results", "_ref/triqs_ctseg.solver.Solver.solve", "_ref/triqs_ctseg.solver.Solver.solve_params", "about", "algorithm_implementation/ctseg", "algorithm_implementation/implementation_notes", "documentation", "guide/measurements", "guide/moves", "guide/step_by_step", "index", "install", "issues"], "filenames": ["ChangeLog.md", "_ref/triqs_ctseg.solver.Solver.rst", "_ref/triqs_ctseg.solver.Solver.D0_tau.rst", "_ref/triqs_ctseg.solver.Solver.Delta_tau.rst", 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19, "issu": 19}, "envversion": {"sphinx.domains.c": 3, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 9, "sphinx.domains.index": 1, "sphinx.domains.javascript": 3, "sphinx.domains.math": 2, "sphinx.domains.python": 4, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.intersphinx": 1, "sphinx.ext.todo": 2, "sphinx.ext.viewcode": 1, "sphinx": 60}, "alltitles": {"Changelog": [[0, "changelog"]], "Version 3.2.0": [[0, "version-3-2-0"]], "triqs_ctseg.solver.Solver": [[1, "triqs-ctseg-solver-solver"]], "triqs_ctseg.solver.Solver.D0_tau": [[2, "triqs-ctseg-solver-solver-d0-tau"]], "triqs_ctseg.solver.Solver.Delta_tau": [[3, "triqs-ctseg-solver-solver-delta-tau"]], "triqs_ctseg.solver.Solver.Jperp_tau": [[4, "triqs-ctseg-solver-solver-jperp-tau"]], "triqs_ctseg.solver.Solver.__init__": [[5, "triqs-ctseg-solver-solver-init"]], "Parameters": [[5, "parameters"], [8, "parameters"]], "triqs_ctseg.solver.Solver.constr_params": [[6, "triqs-ctseg-solver-solver-constr-params"]], "triqs_ctseg.solver.Solver.results": [[7, "triqs-ctseg-solver-solver-results"]], "triqs_ctseg.solver.Solver.solve": [[8, "triqs-ctseg-solver-solver-solve"]], "triqs_ctseg.solver.Solver.solve_params": [[9, "triqs-ctseg-solver-solver-solve-params"]], "About CTSEG": [[10, "about-ctseg"]], "The CTSEG double expansion algorithm": [[11, "the-ctseg-double-expansion-algorithm"]], "Double expansion": [[11, "double-expansion"]], "Configuration": [[11, "configuration"], [12, "configuration"]], "Sign": [[11, "sign"]], "Implementation notes": [[12, "implementation-notes"]], "Solver core": [[12, "solver-core"]], "Inputs": [[12, "inputs"]], "Imaginary time points": [[12, "imaginary-time-points"]], "Work data": [[12, "work-data"]], "Determinants": [[12, "determinants"]], "Miscellaneous": [[12, "miscellaneous"]], "Documentation": [[13, "documentation"]], "Algorithm and implementation": [[13, "algorithm-and-implementation"]], "User guide": [[13, "user-guide"]], "Python reference manual": [[13, "python-reference-manual"]], "Measurements": [[14, "measurements"]], "Imaginary time Green\u2019s function": [[14, "imaginary-time-green-s-function"]], "Self-energy improved estimator": [[14, "self-energy-improved-estimator"]], "Density": [[14, "density"]], "Static density correlation function": [[14, "static-density-correlation-function"]], "Dynamic density correlation function": [[14, "dynamic-density-correlation-function"]], "Perpendicular spin-spin correlation function": [[14, "perpendicular-spin-spin-correlation-function"]], "State histogram": [[14, "state-histogram"]], "Average sign": [[14, "average-sign"]], "Perturbation order histograms": [[14, "perturbation-order-histograms"]], "Monte Carlo moves": [[15, "monte-carlo-moves"]], "Insert segment": [[15, "insert-segment"]], "Remove segment": [[15, "remove-segment"]], "Split segment": [[15, "split-segment"]], "Regroup segment": [[15, "regroup-segment"]], "Move segment": [[15, "move-segment"]], "Insert spin segment": [[15, "insert-spin-segment"]], "Remove spin segment": [[15, "remove-spin-segment"]], "Swap spin lines": [[15, "swap-spin-lines"]], "Split spin segment": [[15, "split-spin-segment"]], "Regroup spin segment": [[15, "regroup-spin-segment"]], "Step-by-step guide": [[16, "step-by-step-guide"]], "Step 1 - Choose the construction parameters": [[16, "step-1-choose-the-construction-parameters"]], "Green\u2019s function structure": [[16, "green-s-function-structure"]], "Step 2 - Construct the solver": [[16, "step-2-construct-the-solver"]], "Step 3 - Supply the solver inputs": [[16, "step-3-supply-the-solver-inputs"]], "Local Hamiltonian": [[16, "local-hamiltonian"]], "Quadratic part": [[16, "quadratic-part"]], "Quartic part": [[16, "quartic-part"]], "Hybridization function": [[16, "hybridization-function"]], "Dynamical density-density interaction": [[16, "dynamical-density-density-interaction"]], "Spin-spin interaction": [[16, "spin-spin-interaction"]], "Solve parameters": [[16, "solve-parameters"]], "Step 4 - Run the solver": [[16, "step-4-run-the-solver"]], "Step 5 - Access the results": [[16, "step-5-access-the-results"]], "Step 6 - Save the results": [[16, "step-6-save-the-results"]], "Running the solver in parallel": [[16, "running-the-solver-in-parallel"]], "The Segment Picture Solver": [[17, "the-segment-picture-solver"]], "CTSEG 3.3.0": [[17, null]], "Install CTSEG": [[18, "install-ctseg"]], "Compiling CTSEG from source": [[18, "compiling-ctseg-from-source"]], "Prerequisites": [[18, "prerequisites"]], "Installation steps": [[18, "installation-steps"]], "Version compatibility": [[18, "version-compatibility"]], "Custom CMake options": [[18, "custom-cmake-options"]], "Reporting issues": [[19, "reporting-issues"]]}, "indexentries": {"solver (class in triqs_ctseg.solver)": [[1, "triqs_ctseg.solver.Solver"]], "d0_tau (triqs_ctseg.solver.solver attribute)": [[2, "triqs_ctseg.solver.Solver.D0_tau"]], "delta_tau (triqs_ctseg.solver.solver attribute)": [[3, "triqs_ctseg.solver.Solver.Delta_tau"]], "jperp_tau (triqs_ctseg.solver.solver attribute)": [[4, "triqs_ctseg.solver.Solver.Jperp_tau"]], "__init__() (triqs_ctseg.solver.solver method)": [[5, "triqs_ctseg.solver.Solver.__init__"]], "constr_params (triqs_ctseg.solver.solver attribute)": [[6, "triqs_ctseg.solver.Solver.constr_params"]], "results (triqs_ctseg.solver.solver attribute)": [[7, "triqs_ctseg.solver.Solver.results"]], "solve() (triqs_ctseg.solver.solver method)": [[8, "triqs_ctseg.solver.Solver.solve"]], "solve_params (triqs_ctseg.solver.solver attribute)": [[9, "triqs_ctseg.solver.Solver.solve_params"]]}}) \ No newline at end of file
\[\begin{split}\begin{split} \mathcal{S} &= \iint_0^{\beta} \mathrm{d} \tau \mathrm{d} \tau' \sum_{a,b} \left\{ \overline{c}_{a\sigma} (\tau) -\left( (\partial_{\tau} + \epsilon_{a\sigma})\delta_{ab}^{\sigma \sigma'} \delta_{\tau - \tau'} + \Delta_{ab}^{\sigma \sigma'}(\tau - \tau')\right) +\left( (\partial_{\tau} + \epsilon_{a\sigma} - \mu)\delta_{ab}^{\sigma \sigma'} \delta_{\tau - \tau'} + \Delta_{ab}^{\sigma \sigma'}(\tau - \tau')\right) c_{b\sigma'}(\tau') \right\} \\ &+ \frac{1}{2} \iint_0^{\beta} \mathrm{d} \tau \mathrm{d} \tau' \sum_{a,b} \mathcal{U}_{ab}(\tau - \tau') n_a(\tau) n_b(\tau') + \frac{1}{2} \iint_0^{\beta} \mathrm{d} \tau \mathrm{d} \tau' \sum_{a, \xi = x, y, z} s_a^{\xi}(\tau) \mathcal{J}_a^{\xi}(\tau - \tau') s_a^{\xi} (\tau') @@ -232,7 +231,8 @@ creation and annihilation operators on the impurity, respectively. \(\Delta_{ab}^{\sigma \sigma'}(\tau)\) is the hybridization function, that accounts for particle exchange between the impurity and the bath, and \(\mathcal{U}_{ab} (\tau)\) and \(\mathcal{J}_{a}^{\xi} (\tau)\) are the (dynamical) -density-density and spin-spin interactions, respectively. +density-density and spin-spin interactions, respectively. The \(\epsilon_{a\sigma}\) are orbital energies and \(mu\) +is the chemical potential.The CTSEG solver carries out a double expansion in the hybridization term and in the perpendicular spin-spin interaction term to obtain the fully interacting impurity Green’s function \(G(\tau)\) and a range of other observables. Learn how to use it in the Documentation.
diff --git a/ctseg/3.3.x/install.html b/ctseg/3.3.x/install.html index 54c30a542a..a61915d34c 100644 --- a/ctseg/3.3.x/install.html +++ b/ctseg/3.3.x/install.html @@ -86,9 +86,8 @@
Step 1 - Choose the construction parameters"gf_struct": gf_struct, "beta": 100, "n_tau": 1001, - "n_tau_k": 1001 + "n_tau_bosonic": 1001 }
Green’s function structure
@@ -260,11 +267,28 @@Step 2 - Construct the solver
Step 3 - Supply the solver inputs
We now need to provide the solver with the parameters of the action that define the impurity problem. -Here, we will give examples for a single-orbital impurity (
-gf_struct = [("up", 1), ("down", 1)]).- Interaction Hamiltonian
-The static part of the electron-electron interaction is supplied as a TRIQS operator. In the CTSEG case, -it is always a density-density interaction. Density operators are represented by
+n(block_name, orbital_number). +Here, we will give examples for a single-orbital impurity (gf_struct = [("up", 1), ("down", 1)]). +The CTSEG input structure is similar to the CTHYB Delta interface. +The time-independent part of the action (i.e., the local Hamiltonian) is supplied as a TRIQS many-body operator, and the time-dependent parts +are supplied as the appropriate type of TRIQS Green’s functions.+ Local Hamiltonian
+The impurity problem must be supplied to CTSEG in the basis where the quadratic part of the local Hamiltonian is diagonal.
++ +Quadratic part
+In its eigenbasis, the quadratic part of the local Hamiltonian
+h_loc0is +proportional to the density operator. Density operators are represented byn(block_name, orbital_number). +For our single orbital problem:++from triqs.operators import * +h_loc0 = (eps - mu) * (n("up", 0) + n("down", 0)) +
Here,
+epsis the orbital energy andmuthe chemical potential. +The interaction Hamiltonian is passed to the solver as part of the solve parameters (see below).+ Quartic part
+In the impurity problems handled by CTSEG, the quartic part of the local Hamiltonian is always a density-density interaction. For our single orbital problem:
-from triqs.operators import * h_int = U * n("up", 0) * n("down", 0) @@ -290,6 +314,7 @@
Interaction Hamiltonian
The interaction Hamiltonian is passed to the solver as part of the solve parameters (see below).
+Hybridization function
The CTSEG solver takes as an input the hybridization function \(\Delta(\tau)\) that appears in the @@ -313,11 +338,13 @@
Hybridization function
S.Delta_tau << Delta_tau
This is different from the CTHYB solver, which takes as input the non-interacting impurity -Green’s function \(G_0(i\omega_n)\). It is defined as
+The value of
+n_tausupplied in theconstr_paramsand the number of points in the \(\tau\) grid of +the \(\Delta(\tau)\) input must match.This is different from the default interface of the CTHYB solver, +which takes as input the non-interacting impurity Green’s function \(G_0(i\omega_n)\). It is defined as
\[G_0(i \omega_n) = \frac{1}{i \omega_n - \hat h_0 - \Delta(i \omega_n)}\]-where \(\hat h_0\) is the non-interacting impurity Hamiltonian. Note that \(\Delta(i\omega_n)\) vanishes in the high frequency limit. +
where \(\hat h_0\) is the quadratic part of the local Hamiltonian. Note that \(\Delta(i\omega_n)\) vanishes in the high frequency limit. The following code extracts from a
BlockGfG0_iwaBlockGfDelta_iwand a matrixh0for each block:-def get_h0_Delta(G0_iw): h0_lst, Delta_iw = [], G0_iw.copy() @@ -331,14 +358,6 @@
Hybridization functionh0_lst, Delta_iw = get_h0_Delta(G0_iw)
The eigenvalues of the
-h0provide the orbital dependent chemical potential (orbital energies):-import numpy as np -from numpy import linalg -mu_list = [] -for h0 in h0_lst: - mu_list += [-l for l in linalg.eig(h0)[0].real] -
If the
h0are already expressed in the local eigenbasis, the obtained hybridization function can be directly used as the solver input. In the general case, they need to be rotated to the eigenbasis:-rot_lst = [np.matrix(linalg.eig(h0_bl)[1]) for h0_bl in h0] @@ -346,38 +365,40 @@
Hybridization functiong0_bl << rot_bl.H * g0_bl * rot_bl
If a rotation is required, then the interactions should also be rotated accordingly.
- -- Chemical potential
-The orbital-dependent chemical potential is passed to the solver as the solve parameter
-chemical_potential(see below), -a list with one value per color. For example, for the single-orbital problem:chemical_potential = [mu, mu] +
If a rotation is required, then the interactions should also be rotated accordingly. +The non-interacting Hamiltonian operator in its eigenbasis is obtained as:
+-import numpy as np +from numpy import linalg +for i, (bl_name, bl_size) in enumerate(gf_struct): + for j in range bl_size: + if (i == 0 and j == 0): + hloc_0 = linalg.eig(h0_lst[i])[0][j].real * n(bl_name, j) + else: + hloc_0 += linalg.eig(h0_lst[i])[0][j].real * n(bl_name, j)
-Note
-This is different from the Delta interface in CTHYB, which takes
-h0(supplied as TRIQS operator) as an input.Dynamical density-density interaction
The dynamical density-density interaction \(D(\tau)\) (see CTSEG algorithm) is initialized as:
-D_tau = GfImTime(indices = range(n_colors), beta = beta, statistic = "Boson", n_points = n_tau_k) +
-tau_mesh = MeshImTime(beta, 'Boson', n_tau_bosonic) +D_tau = Block2Gf(mesh = tau_mesh, gf_struct = gf_struct)
It is a matrix Green’s function, for which no block structure is explicitly enforced.
---Note
-The ordering of the rows and columns in
-D_tauis consistent with the ordering of the blocks inDelta_tau.The data in
D_taucan be specified manually (D_tau.data = ...) or by using an analytical expression. +It is a two-block-index Green’s function, since the dynamical interaction does not necessarily have the same block +diagonal structure as the hybridization function.
+The data in
D_taucan be specified manually (D_tau["block1", "block2"].data = ...) or by using an analytical expression. For example:from triqs.gf.descriptors import Function wp = 1 -D_iw = GfImFreq(indices = range(n_colors), beta = beta, statistic = "Boson", n_points = n_tau_k//2) +D_iw = GfImFreq(indices = [0], beta = beta, statistic = "Boson", n_points = n_tau_bosonic//2) +d_tau = GfImTime(indices = [0], beta = beta, statistic = "Boson", n_points = n_tau_bosonic) D_iw << Function(lambda w: wp**2 / (w**2 - wp**2)) -D_tau << Fourier(D_iw) +d_tau << Fourier(D_iw) +D_tau["up", "up"] << d_tau +D_tau["up", "down"] << d_tau +D_tau["down", "up"] << d_tau +D_tau["down", "down"] << d_tau
The dynamical interaction is supplied to the solver via:
@@ -388,10 +409,11 @@Dynamical density-density interaction
Spin-spin interaction
The perpendicular spin-spin interaction \(J_{\perp}(\tau)\) (see CTSEG algorithm) is initialized as:
-Jperp_tau = GfImTime(indices = [0], beta = beta, statistic = "Boson", n_points = n_tau_k) +
-Jperp_tau = GfImTime(indices = [0], beta = beta, statistic = "Boson", n_points = n_tau_bosonic)
It is a \(1 \times 1\) matrix Green’s function. It is supplied to the solver via:
+It is a \(1 \times 1\) matrix Green’s function, since perpendicular spin-spin interactions are +only implemented for a single orbital. It is supplied to the solver via:
@@ -401,12 +423,14 @@S.Jperp_tau << Jperp_tau
Spin-spin interaction
The solver is then accordingly set up as:
+S.Jperp_tau << Q_tau -S.D0_tau[0, 0] << D_tau + (1/4) * Q_tau[0, 0] -S.D0_tau[0, 1] << D_tau - (1/4) * Q_tau[0, 0] -S.D0_tau[1, 0] << D_tau - (1/4) * Q_tau[0, 0] -S.D0_tau[1, 1] << D_tau + (1/4) * Q_tau[0, 0] +S.D0_tau["up", "up"] << (1/4) * Q_tau +S.D0_tau["up", "down"] << - (1/4) * Q_tau +S.D0_tau["down", "up"] << - (1/4) * Q_tau +S.D0_tau["down", "down"] << (1/4) * Q_tau
The value of
n_tau_bosonicsupplied in theconstr_paramsand the number of points in the \(\tau\) grids of +the \(D(\tau)\) and \(J_{\perp}(\tau)\) inputs must match.Solve parameters
@@ -414,7 +438,7 @@Solve parameters
-solve_params = { "h_int": h_int, - "chemical_potential": chemical_potential, + "h_loc0": h_loc0, "length_cycle": 50, "n_warmup_cycles": 20000, "n_cycles": 200000 @@ -423,7 +447,7 @@
Solve parameters
Solve parameters
solve_params["measure_F_tau"] = True.The complete list of parameters is available here.
@@ -445,12 +471,6 @@Step 4 - Run the solver
S.solve(**solve_params)
-Warning
-The solver prints to the command line the interaction matrix
-Uand chemical potentialmuthat are used internally. -In the presence of dynamical interactions, these are renormalized values, different from the input parameters contained -inh_intandchemical_potential(see CTSEG algorithm).After it is done accumulating, the solver prints the average acceptance rates. Very low acceptance rates for all moves (below 0.01) are generally a sign that something went wrong. However, some of the moves (
@@ -470,14 +490,14 @@split_spin_segment,regroup_spin_segment) often have low acceptance rates, even if the calculation runs as it should.Step 5 - Access the results\(\chi(\tau) = (1/3) \sum_{i = x, y, z} \langle s_i(\tau) s_i(0) \rangle\) can be obtained from the density-density correlation function:
nn_tau = S.results.nn_tau -chi_tau = 0.25 * (nn_tau[0, 0] + nn_tau[1, 1] - nn_tau[0, 1] - nn_tau[1, 0]) +chi_tau = 0.25 * (nn_tau["up", "up"] + nn_tau["down", "down"] - nn_tau["up", "down"] - nn_tau["down", "up"])
If rotational invariance is broken (for instance, in the presence of a Zeeman field), one needs to measure separately the perpendicular spin-spin correlation function:
nn_tau = S.results.nn_tau sperp_tau = S.results.sperp_tau -chi_tau = (0.25 * (nn_tau[0, 0] + nn_tau[1, 1] - nn_tau[0, 1] - nn_tau[1, 0]) + 2*sperp_tau[0, 0]) / 3 +chi_tau = (0.25 * (nn_tau["up", "up"] + nn_tau["down", "down"] - nn_tau["up", "down"] - nn_tau["down", "up"]) + 2*sperp_tau) / 3
triqs_ctseg.solver.Solver.constr_params
n_tau_k
n_tau_bosonic
int
10001
Number of time slices for bosonic functions
chemical_potential
nda::vector<double>
nda::vector<double>{}
Chemical potential (high frequency limit of \(G_0^{-1}(i\omega) - i \omega\))
h_loc0
triqs::operators::many_body_operator
–
Quandratic part of the local Hamiltonian (including chemical potential)
n_tau_G
int
0
Number of points on which to measure G(tau)/F(tau) (defaults to n_tau)
n_tau_chi2
int
0
Number of points on which to measure 2-point functions (defaults to n_tau_bosonic)
n_cycles
int
Parameters
measure_perturbation_order_histograms
measure_pert_order
bool
true
Whether to measure the perturbation order histograms (order in Delta and Jperp)
measure_gt
measure_G_tau
bool
true
Whether to measure G(tau) (see [[measure_g_f_tau]])
Whether to measure G(tau) (see measures/G_F_tau)
measure_ft
measure_F_tau
bool
false
Whether to measure F(tau) (see [[measure_g_f_tau]])
Whether to measure F(tau) (see measures/G_F_tau)
measure_n
measure_densities
bool
true
Whether to measure density (see [[measure_density]])
Whether to measure densities (see measures/densities)
measure_sign
measure_average_sign
bool
true
Whether to measure sign (see [[measure_sign]])
Whether to measure the average sign (see measures/average_sign)
measure_nn
measure_nn_static
bool
false
Whether to measure <n(0)n(0)> (see [[measure_nn]])
Whether to measure <n(0)n(0)> (see measures/nn_static)
measure_nnt
measure_nn_tau
bool
false
Whether to measure <n(tau)n(0)> (see [[measure_nnt]])
Whether to measure <n(tau)n(0)> (see measures/nn_tau)
measure_sperpt
measure_Sperp_tau
bool
false
Whether to measure <s_x(tau)s_x(0)> (see [[measure_sperp_tau]])
Whether to measure <S_x(tau)S_x(0)> (see measures/Sperp_tau)
measure_statehist
measure_state_hist
bool
false
Whether to measure state histograms (see [[measure_statehist]])
Whether to measure state histograms (see measures/state_hist)
det_init_size
int
chemical_potential
nda::vector<double>
nda::vector<double>{}
Chemical potential (high frequency limit of \(G_0^{-1}(i\omega) - i \omega\))
h_loc0
triqs::operators::many_body_operator
–
Quandratic part of the local Hamiltonian (including chemical potential)
n_tau_G
int
0
Number of points on which to measure G(tau)/F(tau) (defaults to n_tau)
n_tau_chi2
int
0
Number of points on which to measure 2-point functions (defaults to n_tau_bosonic)
n_cycles
int
triqs_ctseg.solver.Solver.solve_params
measure_perturbation_order_histograms
measure_pert_order
bool
true
Whether to measure the perturbation order histograms (order in Delta and Jperp)
measure_gt
measure_G_tau
bool
true
Whether to measure G(tau) (see [[measure_g_f_tau]])
Whether to measure G(tau) (see measures/G_F_tau)
measure_ft
measure_F_tau
bool
false
Whether to measure F(tau) (see [[measure_g_f_tau]])
Whether to measure F(tau) (see measures/G_F_tau)
measure_n
measure_densities
bool
true
Whether to measure density (see [[measure_density]])
Whether to measure densities (see measures/densities)
measure_sign
measure_average_sign
bool
true
Whether to measure sign (see [[measure_sign]])
Whether to measure the average sign (see measures/average_sign)
measure_nn
measure_nn_static
bool
false
Whether to measure <n(0)n(0)> (see [[measure_nn]])
Whether to measure <n(0)n(0)> (see measures/nn_static)
measure_nnt
measure_nn_tau
bool
false
Whether to measure <n(tau)n(0)> (see [[measure_nnt]])
Whether to measure <n(tau)n(0)> (see measures/nn_tau)
measure_sperpt
measure_Sperp_tau
bool
false
Whether to measure <s_x(tau)s_x(0)> (see [[measure_sperp_tau]])
Whether to measure <S_x(tau)S_x(0)> (see measures/Sperp_tau)
measure_statehist
measure_state_hist
bool
false
Whether to measure state histograms (see [[measure_statehist]])
Whether to measure state histograms (see measures/state_hist)
det_init_size
int
` can be switched on and off. Some of the measurements (self-energy improved estimator, density correlation functions) can be time-consuming, and they are off by default. For example, to turn the improved estimator - measurement on, one should set ``solve_params["measure_ft"] = True``. + measurement on, one should set ``solve_params["measure_F_tau"] = True``. * **Move control**. All the :doc:`Monte Carlo moves ` can be switched on and off. This functionality exists to facilitate testing - for developers. The solver chooses the relevant moves depending on its inputs, and regular users should not need move control. + for developers. The solver chooses the relevant moves depending on its inputs, and regular users should not need move control. + +* Optional sample numbers for the measured two-point functions: ``n_tau_G`` (defaults to ``n_tau``) for fermionic functions + and ``n_tau_chi2`` (defaults to ``n_tau_bosonic``) for bosonic functions. The complete list of parameters is available :doc:`here <../_ref/triqs_ctseg.solver.Solver.solve>`. @@ -260,11 +289,6 @@ The CTQMC run is triggered by:: S.solve(**solve_params) -.. warning:: - The solver prints to the command line the interaction matrix ``U`` and chemical potential ``mu`` that are used internally. - In the presence of dynamical interactions, these are renormalized values, different from the input parameters contained - in ``h_int`` and ``chemical_potential`` (see :doc:`CTSEG algorithm <../algorithm_implementation/ctseg>`). - After it is done accumulating, the solver prints the average acceptance rates. Very low acceptance rates for all moves (below 0.01) are generally a sign that something went wrong. However, some of the moves (``split_spin_segment``, ``regroup_spin_segment``) often have low acceptance rates, even if the calculation runs as it should. @@ -286,14 +310,14 @@ For a rotationally-invariant impurity, the spin-spin correlation function :math: correlation function:: nn_tau = S.results.nn_tau - chi_tau = 0.25 * (nn_tau[0, 0] + nn_tau[1, 1] - nn_tau[0, 1] - nn_tau[1, 0]) + chi_tau = 0.25 * (nn_tau["up", "up"] + nn_tau["down", "down"] - nn_tau["up", "down"] - nn_tau["down", "up"]) If rotational invariance is broken (for instance, in the presence of a Zeeman field), one needs to measure separately the perpendicular spin-spin correlation function:: nn_tau = S.results.nn_tau sperp_tau = S.results.sperp_tau - chi_tau = (0.25 * (nn_tau[0, 0] + nn_tau[1, 1] - nn_tau[0, 1] - nn_tau[1, 0]) + 2*sperp_tau[0, 0]) / 3 + chi_tau = (0.25 * (nn_tau["up", "up"] + nn_tau["down", "down"] - nn_tau["up", "down"] - nn_tau["down", "up"]) + 2*sperp_tau) / 3 Step 6 - Save the results ************************* diff --git a/ctseg/3.3.x/_sources/index.rst.txt b/ctseg/3.3.x/_sources/index.rst.txt index ea88d15e64..0d3debf07b 100644 --- a/ctseg/3.3.x/_sources/index.rst.txt +++ b/ctseg/3.3.x/_sources/index.rst.txt @@ -14,7 +14,7 @@ The imaginary time action solved by CTSEG is of the form \begin{split} \mathcal{S} &= \iint_0^{\beta} \mathrm{d} \tau \mathrm{d} \tau' \sum_{a,b} \left\{ \overline{c}_{a\sigma} (\tau) - \left( (\partial_{\tau} + \epsilon_{a\sigma})\delta_{ab}^{\sigma \sigma'} \delta_{\tau - \tau'} + \Delta_{ab}^{\sigma \sigma'}(\tau - \tau')\right) + \left( (\partial_{\tau} + \epsilon_{a\sigma} - \mu)\delta_{ab}^{\sigma \sigma'} \delta_{\tau - \tau'} + \Delta_{ab}^{\sigma \sigma'}(\tau - \tau')\right) c_{b\sigma'}(\tau') \right\} \\ &+ \frac{1}{2} \iint_0^{\beta} \mathrm{d} \tau \mathrm{d} \tau' \sum_{a,b} \mathcal{U}_{ab}(\tau - \tau') n_a(\tau) n_b(\tau') + \frac{1}{2} \iint_0^{\beta} \mathrm{d} \tau \mathrm{d} \tau' \sum_{a, \xi = x, y, z} s_a^{\xi}(\tau) \mathcal{J}_a^{\xi}(\tau - \tau') s_a^{\xi} (\tau') @@ -37,7 +37,8 @@ and :math:`c_{a\sigma}(\tau)` are the :math:`\beta`-antiperiodic Grassmann field creation and annihilation operators on the impurity, respectively. :math:`\Delta_{ab}^{\sigma \sigma'}(\tau)` is the hybridization function, that accounts for particle exchange between the impurity and the bath, and :math:`\mathcal{U}_{ab} (\tau)` and :math:`\mathcal{J}_{a}^{\xi} (\tau)` are the (dynamical) -density-density and spin-spin interactions, respectively. +density-density and spin-spin interactions, respectively. The :math:`\epsilon_{a\sigma}` are orbital energies and :math:`mu` +is the chemical potential. The CTSEG solver carries out a double expansion in the hybridization term and in the perpendicular spin-spin interaction term to obtain the fully interacting impurity Green's function :math:`G(\tau)` and a range of diff --git a/ctseg/3.3.x/about.html b/ctseg/3.3.x/about.html index 16a375cf05..54a002511c 100644 --- a/ctseg/3.3.x/about.html +++ b/ctseg/3.3.x/about.html @@ -85,9 +85,8 @@ solve_paramsas part of the interaction Hamiltonian. It should be supplied as a TRIQSBlock2Gf+(since it is no necessarily block-diagonal likeDelta_tau).
Parametersn_tau_k
n_tau_bosonic
int
10001
Number of time slices for bosonic functions
n_tau_k
n_tau_bosonic
int
10001
Number of time slices for bosonic functions