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V1.3.1 (#21)
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* Ensures symmetries are enforced at all times. The previous implementation would turn gf[:,:,t1,t2] = a into gf[i,j,t1,t2] = a[i,j] for all (i,j) which did not enforce the SkewHermitian symmetry as the adjoint operation would be taken element-wise

* adjust notebooks to new kbsolve

---------

Co-authored-by: Francisco Meirinhos <[email protected]>
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@timbode @fmeirinhos
timbode and fmeirinhos authored Mar 17, 2024
1 parent 54eee03 commit 1481ad6
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2 changes: 1 addition & 1 deletion Project.toml
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Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
name = "KadanoffBaym"
uuid = "82532805-809c-4ef0-842b-4b00c5e9be5f"
authors = ["Francisco Meirinhos, Tim Bode"]
version = "1.3"
version = "1.3.1"

[deps]
AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"
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45 changes: 22 additions & 23 deletions examples/fermi-hubbard-2B.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -28,7 +28,7 @@
"using JLD\n",
"\n",
"using PyPlot\n",
"PyPlot.plt.style.use(\"./paper.mplstyle\")\n",
"# PyPlot.plt.style.use(\"./paper.mplstyle\")\n",
"using LaTeXStrings"
]
},
Expand Down Expand Up @@ -360,7 +360,6 @@
"outputs": [],
"source": [
"let\n",
" Gs = loaded_sol[\"solution\"]\n",
" num_points = loaded_sol[\"solution\"].t |> length\n",
" \n",
" xpad = 8\n",
Expand All @@ -370,10 +369,10 @@
" idx_1 = 1\n",
" idx_2 = 8\n",
"\n",
" ax1.plot(loaded_sol[\"solution\"].t, [imag(loaded_sol[\"solution\"].u[1][idx_1, idx_1, k, k] .+ loaded_sol[\"solution\"].u[3][idx_1, idx_1, k, k]) for k = 1:num_points], \n",
" ax1.plot(loaded_sol[\"solution\"].t, [imag(data.GL_u.data[idx_1, idx_1, k, k] .+ data.GL_d.data[idx_1, idx_1, k, k]) for k = 1:num_points], \n",
" label = \"\\$ i=1\\$\", lw=1.5, ls = \"--\", c = \"#438E6A\")\n",
"\n",
" ax1.plot(loaded_sol[\"solution\"].t, [imag(loaded_sol[\"solution\"].u[1][idx_2, idx_2, k, k] .+ loaded_sol[\"solution\"].u[3][idx_2, idx_2, k, k]) for k = 1:num_points], \n",
" ax1.plot(loaded_sol[\"solution\"].t, [imag(data.GL_u.data[idx_2, idx_2, k, k] .+ data.GL_d.data[idx_2, idx_2, k, k]) for k = 1:num_points], \n",
" label = \"\\$ i=8\\$\", lw=1.5, ls = \"-\", c = \"#2D5FAA\")\n",
"\n",
" ax1.set_xlim(0, tmax)\n",
Expand All @@ -387,10 +386,10 @@
"\n",
" # ax2 = subplot(122)\n",
"\n",
" ax2.plot(loaded_sol[\"solution\"].t, [imag(loaded_sol[\"solution\"].u[1][idx_1, idx_1, k, k] .- loaded_sol[\"solution\"].u[3][idx_1, idx_1, k, k]) for k = 1:num_points], \n",
" ax2.plot(loaded_sol[\"solution\"].t, [imag(data.GL_u.data[idx_1, idx_1, k, k] .- data.GL_d.data[idx_1, idx_1, k, k]) for k = 1:num_points], \n",
" label = \"\\$ i=2\\$\", lw=1.5, ls = \"--\", c = \"#438E6A\")\n",
"\n",
" ax2.plot(loaded_sol[\"solution\"].t, [imag(loaded_sol[\"solution\"].u[1][idx_2, idx_2, k, k] .- loaded_sol[\"solution\"].u[3][idx_2, idx_2, k, k]) for k = 1:num_points], \n",
" ax2.plot(loaded_sol[\"solution\"].t, [imag(data.GL_u.data[idx_2, idx_2, k, k] .- data.GL_d.data[idx_2, idx_2, k, k]) for k = 1:num_points], \n",
" label = \"\\$ i=2\\$\", lw=1.5, ls = \"-\", c = \"#2D5FAA\")\n",
"\n",
" ax2.set_xlim(0, tmax)\n",
Expand All @@ -407,7 +406,7 @@
" bbox_to_anchor=(0.96, .0, .0, .0),\n",
" bbox_transform=ax1.transAxes)\n",
"\n",
" axins1.plot(loaded_sol[\"solution\"].t, [(tr(loaded_sol[\"solution\"].u[1][k, k]) |> imag) .+ (tr(loaded_sol[\"solution\"].u[3][k, k]) |> imag) for k = 1:num_points] \n",
" axins1.plot(loaded_sol[\"solution\"].t, [(tr(data.GL_u.data[:, :, k, k]) |> imag) .+ (tr(data.GL_d.data[:, :, k, k]) |> imag) for k = 1:num_points] \n",
" .- sum(N_u .+ N_d) .|> abs, \n",
" label = \"\\$ c \\$\", ls = \"-\", c = \"k\")\n",
" axins1.set_xlim(0, tmax)\n",
Expand All @@ -424,14 +423,14 @@
" bbox_to_anchor=(0.96, .0, .0, .0),\n",
" bbox_transform=ax2.transAxes)\n",
"\n",
" axins2.plot(loaded_sol[\"solution\"].t, [(tr(loaded_sol[\"solution\"].u[1][k, k]) |> imag) .- (tr(loaded_sol[\"solution\"].u[3][k, k]) |> imag) for k = 1:num_points] \n",
" axins2.plot(loaded_sol[\"solution\"].t, [(tr(data.GL_u.data[:, :, k, k]) |> imag) .- (tr(data.GL_d.data[:, :, k, k]) |> imag) for k = 1:num_points] \n",
" .- sum(N_u .- N_d) .|> abs, \n",
" label = \"\\$ c \\$\", ls = \"-\", c = \"k\")\n",
" axins2.set_xlim(0, tmax)\n",
" axins2.set_xticks([0, 8, 16, 24, 32])\n",
" axins2.set_yticks([k for k in 0:0.5:1] .* 3e-15)\n",
"# axins2.set_yticks([k for k in 0:0.5:1] .* 3e-15)\n",
" axins2.set_xticklabels([])\n",
" axins2.set_ylim([0.0, 1] .* 3e-15)\n",
" axins2.set_ylim([0.0, 1] .* 12e-15)\n",
" axins2.set_ylabel(L\"S(t) - S_0\", fontdict = Dict(:fontsize=>10))\n",
" axins2.tick_params(axis=\"y\", labelsize=10)\n",
" axins2.yaxis.get_offset_text().set_fontsize(10)\n",
Expand Down Expand Up @@ -473,12 +472,12 @@
"source": [
"let\n",
" # quantum number to look at\n",
" idx = 5\n",
" idx = 1\n",
" shift = 0\n",
"\n",
" ρτ, (τs, ts) = wigner_transform_itp((loaded_sol[\"solution\"].u[2][idx, idx, :, :] - loaded_sol[\"solution\"].u[1][idx, idx, :, :]), \n",
" ρτ, (τs, ts) = wigner_transform_itp((data.GG_u.data[idx, idx, :, :] - data.GL_u.data[idx, idx, :, :]), \n",
" loaded_sol[\"solution\"].t[1+shift:end-shift], fourier=false);\n",
" ρω, (ωs, ts) = wigner_transform_itp((loaded_sol[\"solution\"].u[2][idx, idx, :, :] - loaded_sol[\"solution\"].u[1][idx, idx, :, :]), \n",
" ρω, (ωs, ts) = wigner_transform_itp((data.GG_u.data[idx, idx, :, :] - data.GL_u.data[idx, idx, :, :]), \n",
" loaded_sol[\"solution\"].t[1+shift:end-shift], fourier=true);\n",
" cmap = \"gist_heat\";\n",
" \n",
Expand All @@ -504,7 +503,7 @@
" ax.set_ylabel(\"\\$ A_{11, \\\\uparrow}(T_{\\\\mathrm{max}}/2, \\\\tau)_W \\$\")\n",
"\n",
" ax = subplot(122)\n",
" heatmap = ax.pcolormesh(X, Y, imag(loaded_sol[\"solution\"].u[1][1, 1, :, :]) .- imag(loaded_sol[\"solution\"].u[2][1, 1, :, :]), cmap=cmap, rasterized=true, vmin=vmin, vmax=vmax)\n",
" heatmap = ax.pcolormesh(X, Y, imag(data.GL_u.data[1, 1, :, :]) .- imag(data.GG_u.data[1, 1, :, :]), cmap=cmap, rasterized=true, vmin=vmin, vmax=vmax)\n",
" heatmap.set_edgecolor(\"face\")\n",
" ax.set_aspect(\"equal\")\n",
" cbar = colorbar(mappable=heatmap)\n",
Expand Down Expand Up @@ -542,7 +541,9 @@
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"tmax = 16;\n",
Expand Down Expand Up @@ -606,9 +607,9 @@
" # quantum number to look at\n",
" idx = 1\n",
"\n",
" ρτ, (τs, ts) = wigner_transform_itp((loaded_sol[\"solution\"].u[2].data[idx, idx, :, :] - loaded_sol[\"solution\"].u[1].data[idx, idx, :, :]), \n",
" ρτ, (τs, ts) = wigner_transform_itp((data.GG_u.data[idx, idx, :, :] - data.GL_u.data[idx, idx, :, :]), \n",
" loaded_sol[\"solution\"].t[1:end], fourier=false);\n",
" ρω, (ωs, ts) = wigner_transform_itp((loaded_sol[\"solution\"].u[2].data[idx, idx, :, :] - loaded_sol[\"solution\"].u[1].data[idx, idx, :, :]), \n",
" ρω, (ωs, ts) = wigner_transform_itp((data.GG_u.data[idx, idx, :, :] - data.GL_u.data[idx, idx, :, :]), \n",
" loaded_sol[\"solution\"].t[1:end], fourier=true);\n",
"\n",
" t_scale = 1\n",
Expand Down Expand Up @@ -638,7 +639,7 @@
" vmax = 1.0\n",
"\n",
" ax = subplot(122)\n",
" heatmap = ax.pcolormesh(X, Y, imag(loaded_sol[\"solution\"].u[1].data[1, 1, :, :]) .- imag(loaded_sol[\"solution\"].u[2].data[1, 1, :, :]), cmap=cmap, rasterized=true, vmin=vmin, vmax=vmax)\n",
" heatmap = ax.pcolormesh(X, Y, imag(data.GL_u.data[1, 1, :, :]) .- imag(data.GG_u.data[1, 1, :, :]), cmap=cmap, rasterized=true, vmin=vmin, vmax=vmax)\n",
" heatmap.set_edgecolor(\"face\")\n",
" ax.set_aspect(\"equal\")\n",
" cbar = colorbar(mappable=heatmap)\n",
Expand All @@ -649,8 +650,6 @@
" ax.set_ylim(0, t_scale * tmax)\n",
" ax.set_xlim(0, t_scale * 8)\n",
" ax.set_ylim(0, t_scale * 8)\n",
" # ax.set_xticks(t_scale .* [0, tmax/2, tmax])\n",
" # ax.set_yticks(t_scale .* [0, tmax/2, tmax])\n",
"\n",
" ax.set_xticks(t_scale .* [0, 2, 4, 6, 8])\n",
" ax.set_yticks(t_scale .* [0, 2, 4, 6, 8])\n",
Expand All @@ -671,15 +670,15 @@
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.7.2",
"display_name": "Julia 1.9.4",
"language": "julia",
"name": "julia-1.7"
"name": "julia-1.9"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.7.2"
"version": "1.9.4"
}
},
"nbformat": 4,
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74 changes: 60 additions & 14 deletions examples/fermi-hubbard-TM.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -28,7 +28,7 @@
"outputs": [],
"source": [
"using PyPlot\n",
"PyPlot.plt.style.use(\"./paper.mplstyle\")\n",
"# PyPlot.plt.style.use(\"./paper.mplstyle\")\n",
"using LaTeXStrings"
]
},
Expand Down Expand Up @@ -436,7 +436,48 @@
" stop = x -> (println(\"t: $(x[end])\"); flush(stdout); false)\n",
" );\n",
"\n",
" save(\"FH_3D_T_matrix_sol_U_$(U₀)_tmax_$(tmax)_atol_$(atol)_rtol_$(rtol).jld\", \"solution\", sol)\n",
" save(\"FH_3D_T_matrix_sol_U_$(U₀)_tmax_$(tmax)_atol_$(atol)_rtol_$(rtol).jld\",\n",
" \"solution\", sol,\n",
" \"GFs\", data.GL_u.data .+ data.GL_d.data)\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Second Born approx."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Callback function for the self-energies\n",
"function second_Born!(model, data, times, _, _, t, t′)\n",
" # Unpack data and model\n",
" (; GL_u, GG_u, GL_d, GG_d, ΣL_u, ΣG_u, ΣL_d, ΣG_d) = data\n",
" (; U) = model\n",
" \n",
" # Resize self-energies when Green functions are resized \n",
" if (n = size(GL_u, 3)) > size(ΣL_u, 3)\n",
" resize!(ΣL_u, n)\n",
" resize!(ΣG_u, n)\n",
" resize!(ΣL_d, n)\n",
" resize!(ΣG_d, n) \n",
" end\n",
" \n",
" # The interaction varies as a function of the forward time (t+t')/2\n",
" U_t = U((times[t] + times[t′])/2)\n",
" \n",
" # Define the self-energies\n",
" ΣL_u[t, t′] = U_t^2 .* GL_u[t, t′] .* GL_d[t, t′] .* transpose(GG_d[t′, t])\n",
" ΣL_d[t, t′] = U_t^2 .* GL_u[t, t′] .* GL_d[t, t′] .* transpose(GG_u[t′, t])\n",
" \n",
" ΣG_u[t, t′] = U_t^2 .* GG_u[t, t′] .* GG_d[t, t′] .* transpose(GL_d[t′, t])\n",
" ΣG_d[t, t′] = U_t^2 .* GG_u[t, t′] .* GG_d[t, t′] .* transpose(GL_u[t′, t])\n",
"end"
]
},
Expand Down Expand Up @@ -500,15 +541,13 @@
"metadata": {},
"outputs": [],
"source": [
"loaded_sol = []\n",
"GFs = []\n",
"ts = []\n",
"\n",
"for (i, (rtol, atol)) in enumerate(tols)\n",
" sol = load(\"FH_3D_T_matrix_sol_U_$(U₀)_tmax_$(tmax)_atol_$(atol)_rtol_$(rtol).jld\")\n",
" push!(loaded_sol, sol)\n",
" push!(GFs, sol[\"solution\"].u)\n",
" push!(ts, sol[\"solution\"].t)\n",
" loaded_data = load(\"FH_3D_T_matrix_sol_U_$(U₀)_tmax_$(tmax)_atol_$(atol)_rtol_$(rtol).jld\")\n",
" push!(GFs, loaded_data[\"GFs\"])\n",
" push!(ts, loaded_data[\"solution\"].t)\n",
"end;"
]
},
Expand All @@ -521,7 +560,7 @@
"outputs": [],
"source": [
"xpad = 8\n",
"ypad = 5;\n",
"ypad = 5\n",
"\n",
"figure(figsize = (8, 3))\n",
"\n",
Expand All @@ -535,11 +574,11 @@
"\n",
"plot([], [], label=\"\\$\\\\texttt{rtol}\\$\", c=\"w\")\n",
"for (i, (rtol, atol)) in enumerate(tols)\n",
" plot(ts[i], [imag(GFs[i][1][idx_1, idx_1, k, k] + GFs[i][3][idx_1, idx_1, k, k]) for k in eachindex(ts[i])], \n",
" plot(ts[i], [imag(GFs[i][idx_1, idx_1, k, k]) for k in eachindex(ts[i])], \n",
" label = L\"\\texttt{%$(rtol)}\", lw=1.5, styles[i], ms=ms, c = colors[i])\n",
"end\n",
"\n",
"plot(sol_2B.t, [imag(sol_2B.u[1][idx_1, idx_1, k, k] .+ sol_2B.u[3][idx_1, idx_1, k, k]) for k in eachindex(sol_2B.t)], \n",
"plot(sol_2B.t, [imag(data.GL_u.data[idx_1, idx_1, k, k] .+ data.GL_d.data[idx_1, idx_1, k, k]) for k in eachindex(sol_2B.t)], \n",
" lw=3, ls = \"--\", c = \"k\", alpha=0.75)\n",
"\n",
"xlim(0, tmax)\n",
Expand All @@ -554,7 +593,7 @@
"\n",
"ax = subplot(122)\n",
"for (i, (rtol, atol)) in enumerate(reverse(tols))\n",
" semilogy(ts[i], [tr(GFs[i][1][k, k]) + tr(GFs[i][3][k, k]) |> imag for k in eachindex(ts[i])] .- sum(N_u .+ N_d) .|> abs, \n",
" semilogy(ts[i], [tr(GFs[i][:, :, k, k]) |> imag for k in eachindex(ts[i])] .- sum(N_u .+ N_d) .|> abs, \n",
" ls = ls[i], c = colors[i])\n",
"end\n",
"\n",
Expand All @@ -571,19 +610,26 @@
"tight_layout(pad = 0.1, w_pad = 0.5, h_pad = 0)\n",
"# savefig(\"fermi_hubbard_T_matrix_convergence.pdf\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.7.2",
"display_name": "Julia 1.9.4",
"language": "julia",
"name": "julia-1.7"
"name": "julia-1.9"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.7.2"
"version": "1.9.4"
}
},
"nbformat": 4,
Expand Down
19 changes: 10 additions & 9 deletions src/gf.jl
View file
Original file line number Diff line number Diff line change
Expand Up @@ -57,6 +57,12 @@ julia> gf[i,j] == gf[:,:,...,:,i,j]
julia> gf[i,j,k] == gf[:,:,...,:,i,j,k]
```
In order to ensure a correct behaviour of the symmetries, `setindex!` is only
defined at the level of time coordinates
```julia-repl
julia> gf[i, j] = a # is equivalent to gf[..., i, j] = a[...]
```
Custom symmetries can be implemented via multiple dispatch
```julia-repl
julia> struct MySymmetry <: KadanoffBaym.AbstractSymmetry end
Expand Down Expand Up @@ -97,16 +103,11 @@ Base.eltype(::GreenFunction{T}) where {T} = T
@inline Base.getindex(::GreenFunction{T,N,A,U}, I) where {T,N,A,U} = error("Single indexing not allowed")
Base.@propagate_inbounds Base.getindex(G::GreenFunction{T,N,A,U}, I::Vararg{T1,N1}) where {T,N,A,U,T1,N1} = G.data[ntuple(i -> Colon(), N-N1)..., I...]

@inline Base.setindex!(::GreenFunction{T,N,A,U}, v, I) where {T,N,A,U} = error("Single indexing not allowed")
Base.@propagate_inbounds function Base.setindex!(G::GreenFunction{T,N,A,U}, v, I::Vararg{T1,N1}) where {T,N,A,U,T1,N1}
ts = last2(I...)
jj = front2(I...)
Base.@propagate_inbounds function Base.setindex!(G::GreenFunction{T,N,A,U}, v, i1::Int, i2::Int) where {T,N,A,U}
G.data[ntuple(i -> Colon(), Val(N - 2))..., i1, i2] = v

if ==(ts...)
G.data[ntuple(i -> Colon(), N-N1)..., jj..., ts...] = v
else
G.data[ntuple(i -> Colon(), N-N1)..., jj..., ts...] = v
G.data[ntuple(i -> Colon(), N-N1)..., jj..., reverse(ts)...] = symmetry(U)(v)
if i1 != i2
G.data[ntuple(i -> Colon(), Val(N - 2))..., i2, i1] = symmetry(U)(v)
end
end

Expand Down
37 changes: 16 additions & 21 deletions test/gf.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -48,21 +48,6 @@ end
end

@testset "setindex!" begin
function setindexA(A::AbstractArray)
for i in 1:N, j in 1:i
A[:, :, i, j] = b
if j != i
A[:, :, j, i] = -adjoint(b)
end
end
end

function setindexG(G)
for i in 1:N, j in 1:i
G[i, j] = b
end
end

data = zeros(ComplexF64, N, N, N, N)
gf = GreenFunction(copy(data), SkewHermitian)

Expand All @@ -73,11 +58,21 @@ end
data[:, :, 2, 1] = -adjoint(b)
@test gf.data == data

setindexA(data)
setindexG(gf)
@test gf.data == data
# # this used to fail
# gf[:, :, 2, 1] = b
# data[:, :, 2, 1] = b
# data[:, :, 1, 2] = -adjoint(b)

for i in 1:N, j in 1:i
data[:, :, i, j] = b
if j != i
data[:, :, j, i] = -adjoint(b)
end
end

for i in 1:N, j in 1:i
gf[i, j] = b
end

# using BenchmarkTools
# @show @btime $setindexA($data)
# @show @btime $setindexG($gf)
@test gf.data == data
end

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Registration pull request created: JuliaRegistries/General/103046

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## Breaking changes

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