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22 changes: 11 additions & 11 deletions triqs/3.2.x/_modules/triqs/gf/tools.html
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Expand Up @@ -1732,7 +1732,7 @@ <h1>Source code for triqs.gf.tools</h1><div class="highlight"><pre>
<span class="kn">from</span> <span class="nn">timeit</span> <span class="kn">import</span> <span class="n">default_timer</span> <span class="k">as</span> <span class="n">timer</span>

<div class="viewcode-block" id="inverse">
<a class="viewcode-back" href="../../../documentation/manual/triqs/gfs/py/tools.html#triqs.gf.tools.inverse">[docs]</a>
<a class="viewcode-back" href="../../../documentation/python_api/triqs.gf.tools.inverse.html#triqs.gf.tools.inverse">[docs]</a>
<span class="k">def</span> <span class="nf">inverse</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Return the inverse of its argument, with proper treatement of lazy expressions.</span>
Expand All @@ -1745,7 +1745,7 @@ <h1>Source code for triqs.gf.tools</h1><div class="highlight"><pre>


<div class="viewcode-block" id="conjugate">
<a class="viewcode-back" href="../../../documentation/manual/triqs/gfs/py/tools.html#triqs.gf.tools.conjugate">[docs]</a>
<a class="viewcode-back" href="../../../documentation/python_api/triqs.gf.tools.conjugate.html#triqs.gf.tools.conjugate">[docs]</a>
<span class="k">def</span> <span class="nf">conjugate</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Return the conjugate of a Green&#39;s function</span>
Expand All @@ -1757,7 +1757,7 @@ <h1>Source code for triqs.gf.tools</h1><div class="highlight"><pre>


<div class="viewcode-block" id="transpose">
<a class="viewcode-back" href="../../../documentation/manual/triqs/gfs/py/tools.html#triqs.gf.tools.transpose">[docs]</a>
<a class="viewcode-back" href="../../../documentation/python_api/triqs.gf.tools.transpose.html#triqs.gf.tools.transpose">[docs]</a>
<span class="k">def</span> <span class="nf">transpose</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Return the transpose of a Green&#39;s function</span>
Expand All @@ -1770,7 +1770,7 @@ <h1>Source code for triqs.gf.tools</h1><div class="highlight"><pre>


<div class="viewcode-block" id="delta">
<a class="viewcode-back" href="../../../documentation/manual/triqs/gfs/py/tools.html#triqs.gf.tools.delta">[docs]</a>
<a class="viewcode-back" href="../../../documentation/python_api/triqs.gf.tools.delta.html#triqs.gf.tools.delta">[docs]</a>
<span class="k">def</span> <span class="nf">delta</span><span class="p">(</span><span class="n">g</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Compute Delta_iw from G0_iw.</span>
Expand Down Expand Up @@ -1807,7 +1807,7 @@ <h1>Source code for triqs.gf.tools</h1><div class="highlight"><pre>

<span class="c1"># Determine one of G0_iw, G_iw and Sigma_iw from other two using Dyson&#39;s equation</span>
<div class="viewcode-block" id="dyson">
<a class="viewcode-back" href="../../../documentation/manual/triqs/gfs/py/tools.html#triqs.gf.tools.dyson">[docs]</a>
<a class="viewcode-back" href="../../../documentation/python_api/triqs.gf.tools.dyson.html#triqs.gf.tools.dyson">[docs]</a>
<span class="k">def</span> <span class="nf">dyson</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Solve Dyson&#39;s equation for given two of G0_iw, G_iw and Sigma_iw to yield the third.</span>
Expand Down Expand Up @@ -1835,7 +1835,7 @@ <h1>Source code for triqs.gf.tools</h1><div class="highlight"><pre>


<div class="viewcode-block" id="read_gf_from_txt">
<a class="viewcode-back" href="../../../documentation/manual/triqs/gfs/py/tools.html#triqs.gf.tools.read_gf_from_txt">[docs]</a>
<a class="viewcode-back" href="../../../documentation/python_api/triqs.gf.tools.read_gf_from_txt.html#triqs.gf.tools.read_gf_from_txt">[docs]</a>
<span class="k">def</span> <span class="nf">read_gf_from_txt</span><span class="p">(</span><span class="n">block_txtfiles</span><span class="p">,</span> <span class="n">block_name</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Read a GfReFreq from text files with the format (w, Re(G), Im(G)) for a single block.</span>
Expand Down Expand Up @@ -1873,7 +1873,7 @@ <h1>Source code for triqs.gf.tools</h1><div class="highlight"><pre>


<div class="viewcode-block" id="write_gf_to_txt">
<a class="viewcode-back" href="../../../documentation/manual/triqs/gfs/py/tools.html#triqs.gf.tools.write_gf_to_txt">[docs]</a>
<a class="viewcode-back" href="../../../documentation/python_api/triqs.gf.tools.write_gf_to_txt.html#triqs.gf.tools.write_gf_to_txt">[docs]</a>
<span class="k">def</span> <span class="nf">write_gf_to_txt</span><span class="p">(</span><span class="n">g</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Write a GfReFreq or GfImFreq to in the format (w/iw, Re(G), Im(G)) for a single block.</span>
Expand All @@ -1899,7 +1899,7 @@ <h1>Source code for triqs.gf.tools</h1><div class="highlight"><pre>


<div class="viewcode-block" id="make_zero_tail">
<a class="viewcode-back" href="../../../documentation/manual/triqs/gfs/py/tools.html#triqs.gf.tools.make_zero_tail">[docs]</a>
<a class="viewcode-back" href="../../../documentation/python_api/triqs.gf.tools.make_zero_tail.html#triqs.gf.tools.make_zero_tail">[docs]</a>
<span class="k">def</span> <span class="nf">make_zero_tail</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">n_moments</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Return a container for the high-frequency coefficients of a given Green function initialized to zero.</span>
Expand All @@ -1922,7 +1922,7 @@ <h1>Source code for triqs.gf.tools</h1><div class="highlight"><pre>


<div class="viewcode-block" id="fit_legendre">
<a class="viewcode-back" href="../../../documentation/manual/triqs/gfs/py/tools.html#triqs.gf.tools.fit_legendre">[docs]</a>
<a class="viewcode-back" href="../../../documentation/python_api/triqs.gf.tools.fit_legendre.html#triqs.gf.tools.fit_legendre">[docs]</a>
<span class="k">def</span> <span class="nf">fit_legendre</span><span class="p">(</span><span class="n">g_t</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot; General fit of a noisy imaginary time Green&#39;s function</span>
<span class="sd"> to a low order Legendre expansion in imaginary time.</span>
Expand Down Expand Up @@ -1999,7 +1999,7 @@ <h1>Source code for triqs.gf.tools</h1><div class="highlight"><pre>


<div class="viewcode-block" id="make_delta">
<a class="viewcode-back" href="../../../documentation/manual/triqs/gfs/py/tools.html#triqs.gf.tools.make_delta">[docs]</a>
<a class="viewcode-back" href="../../../documentation/python_api/triqs.gf.tools.make_delta.html#triqs.gf.tools.make_delta">[docs]</a>
<span class="k">def</span> <span class="nf">make_delta</span><span class="p">(</span><span class="n">V</span><span class="p">,</span> <span class="n">eps</span><span class="p">,</span> <span class="n">mesh</span><span class="p">,</span> <span class="n">block_names</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Create a hybridization function from given hoppings and bath energies</span>
Expand Down Expand Up @@ -2060,7 +2060,7 @@ <h1>Source code for triqs.gf.tools</h1><div class="highlight"><pre>


<div class="viewcode-block" id="discretize_bath">
<a class="viewcode-back" href="../../../documentation/manual/triqs/gfs/py/tools.html#triqs.gf.tools.discretize_bath">[docs]</a>
<a class="viewcode-back" href="../../../documentation/python_api/triqs.gf.tools.discretize_bath.html#triqs.gf.tools.discretize_bath">[docs]</a>
<span class="k">def</span> <span class="nf">discretize_bath</span><span class="p">(</span><span class="n">delta_in</span><span class="p">,</span> <span class="n">Nb</span><span class="p">,</span> <span class="n">eps0</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">V0</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-15</span><span class="p">,</span> <span class="n">maxiter</span><span class="o">=</span><span class="mi">10000</span><span class="p">,</span>
<span class="n">cmplx</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">&#39;BFGS&#39;</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
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Expand Up @@ -41,4 +41,4 @@ Documentation
Returns
^^^^^^^

Constant reference to the storage container
Reference to the storage container
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Expand Up @@ -1729,7 +1729,7 @@
</div></blockquote>
<section id="returns">
<h2>Returns<a class="headerlink" href="#returns" title="Link to this heading"></a></h2>
<p>Constant reference to the storage container</p>
<p>Reference to the storage container</p>
</section>
</section>

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2 changes: 1 addition & 1 deletion triqs/3.2.x/searchindex.js

Large diffs are not rendered by default.

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Expand Up @@ -1757,7 +1757,7 @@ <h2>Dynamical mean-field theory<a class="headerlink" href="#Dynamical-mean-field
\Big( \sum_k \frac{1}{i \omega_n + \mu - \epsilon_k - \Sigma_\mathrm{imp}} \Big)^{-1}
+ \Sigma_\mathrm{imp}\]</div>
<p>We solve the quantum impurity for this new <span class="math notranslate nohighlight">\(G_0\)</span> and loop until convergence</p>
<p><img alt="499aeaa06a194ad2bba658f6efcf4fe7" class="no-scaled-link" src="../../../../_images/selfcons.png" style="width: 40%;" /></p>
<p><img alt="6104116e20a3452aac138256bed61cdb" class="no-scaled-link" src="../../../../_images/selfcons.png" style="width: 40%;" /></p>
</section>
<section id="Bethe-lattice-DMFT">
<h2>Bethe lattice DMFT<a class="headerlink" href="#Bethe-lattice-DMFT" title="Link to this heading"></a></h2>
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Expand Up @@ -1721,7 +1721,7 @@
<section id="General-reminder:-Anderson-impurity-model-and-CTHYB-solver">
<h1>General reminder: Anderson impurity model and CTHYB solver<a class="headerlink" href="#General-reminder:-Anderson-impurity-model-and-CTHYB-solver" title="Link to this heading"></a></h1>
<p>In the Anderson impurity model, we decompose the full lattice problem into an interacting site (‘impurity’) hybridised to a bath:</p>
<p><img alt="fc2524481aff4d038eb5b336cb92a107" src="../../../../_images/dmft_bath_impurity.png" /></p>
<p><img alt="1025eb9eee1c43858621228874183184" src="../../../../_images/dmft_bath_impurity.png" /></p>
<dl>
<dt>with the Hamiltonian :nbsphinx-math:<a href="#id1"><span class="problematic" id="id2">`</span></a>begin{align*}</dt><dd><blockquote>
<div><p>H = &amp; color{red}{H_{rm imp}} + color{darkgreen}{H_{rm hyb}} + color{blue}{H_{rm bath}} \
Expand Down
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Expand Up @@ -1722,7 +1722,7 @@ <h1>Valence-Bond DMFT solution of the Hubbard model<a class="headerlink" href="#
<p>.</p>
<p>In the following, we use <span class="math notranslate nohighlight">\(U/t=10\)</span> and <span class="math notranslate nohighlight">\(t'/t=-0.3\)</span>, which are values commonly used for modeling hole-doped cuprates in a single-band framework. All energies (and temperatures) are expressed in units of <span class="math notranslate nohighlight">\(D=4t=1\)</span>, and the doping is denoted by <span class="math notranslate nohighlight">\(\delta\)</span>.</p>
<p>We subdivide the Brillouin Zone into a minimal set of two patches of <strong>equal</strong> area <span class="math notranslate nohighlight">\(P_+\)</span> (even) and <span class="math notranslate nohighlight">\(P_-\)</span> (odd).</p>
<p><img alt="65cc5a6c1934469bac21946e8fc37060" class="no-scaled-link" src="../../../../_images/vb-patching1.png" style="width: 240px; height: 180px;" /></p>
<p><img alt="ae4810ff48a24f9b89b4aa2af0a282b9" class="no-scaled-link" src="../../../../_images/vb-patching1.png" style="width: 240px; height: 180px;" /></p>
<p><span class="math notranslate nohighlight">\(P_+\)</span> is a central square centered at momentum <span class="math notranslate nohighlight">\((0,0)\)</span> and containing the nodal region; the complementary region <span class="math notranslate nohighlight">\(P_{-}\)</span> extends to the edge of the BZ and contains in particular the antinodal region and the <span class="math notranslate nohighlight">\((\pi,\pi)\)</span> momentum.</p>
<div class="nbinput nblast docutils container">
<div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[2]:
Expand Down
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Expand Up @@ -1768,7 +1768,7 @@ <h2>Dynamical mean-field theory<a class="headerlink" href="#Dynamical-mean-field
\Big( \sum_k \frac{1}{i \omega_n + \mu - \epsilon_k - \Sigma_\mathrm{imp}} \Big)^{-1}
+ \Sigma_\mathrm{imp}\]</div>
<p>We solve the quantum impurity for this new <span class="math notranslate nohighlight">\(G_0\)</span> and loop until convergence</p>
<p><img alt="f066863a4e5641e89b16a7534dd7c3bb" class="no-scaled-link" src="../../../../../_images/selfcons1.png" style="width: 40%;" /></p>
<p><img alt="da9038d4376c448cb7646c39159359b4" class="no-scaled-link" src="../../../../../_images/selfcons1.png" style="width: 40%;" /></p>
</section>
<section id="Bethe-lattice-DMFT">
<h2>Bethe lattice DMFT<a class="headerlink" href="#Bethe-lattice-DMFT" title="Link to this heading"></a></h2>
Expand Down Expand Up @@ -1883,7 +1883,7 @@ <h2>Visualizing the Mott transition<a class="headerlink" href="#Visualizing-the-
<section id="Comparison-with-the-literature">
<h2>Comparison with the literature<a class="headerlink" href="#Comparison-with-the-literature" title="Link to this heading"></a></h2>
<p>You can compare the result above with what can be found in the literature (review of Antoine Georges et al.)</p>
<p><img alt="019e5b1c67144c95b743be13fbd32cb0" class="no-scaled-link" src="../../../../../_images/mott.png" style="width: 30%;" /></p>
<p><img alt="230ad27a4f2b4b9b8d1ea0eed20bb26c" class="no-scaled-link" src="../../../../../_images/mott.png" style="width: 30%;" /></p>
</section>
</section>

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Expand Up @@ -1996,7 +1996,7 @@ <h2>Solution 6<a class="headerlink" href="#Solution-6" title="Link to this headi
</div>
</div>
<p>The result is completely wrong. This is because of the noise in the Monte Carlo data. One would have to make much longer runs in order to reduce the error bars. The Pade approximation can be used only on very accurate data. When the noise is still quite large, one has to use different analytical continuation methods, like MaxEnt, which produces the following spectral function:</p>
<p><img alt="fdbcd830d3b4494280c569fe1c4207d0" src="../../../../../_images/maxent_Aw.png" /></p>
<p><img alt="25b345183d6e45fe8624130d622fddb6" src="../../../../../_images/maxent_Aw.png" /></p>
<p>Regardless of which package you use for MaxEnt, it is very important to remember that there are some important knobs with which one can play in MaxEnt that can substantially change the results, and so one must be very careful in its use!</p>
<blockquote>
<div><p>Exercise 7</p>
Expand Down
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Expand Up @@ -1726,7 +1726,7 @@ <h1>Valence-Bond DMFT solution of the Hubbard model<a class="headerlink" href="#
<p>.</p>
<p>In the following, we use <span class="math notranslate nohighlight">\(U/t=10\)</span> and <span class="math notranslate nohighlight">\(t'/t=-0.3\)</span>, which are values commonly used for modeling hole-doped cuprates in a single-band framework. All energies (and temperatures) are expressed in units of <span class="math notranslate nohighlight">\(D=4t=1\)</span>, and the doping is denoted by <span class="math notranslate nohighlight">\(\delta\)</span>.</p>
<p>We subdivide the Brillouin Zone into a minimal set of two patches of <strong>equal</strong> area <span class="math notranslate nohighlight">\(P_+\)</span> (even) and <span class="math notranslate nohighlight">\(P_-\)</span> (odd).</p>
<p><img alt="19c0544617314019876a93dd4ae0fc09" class="no-scaled-link" src="../../../../../_images/vb-patching.png" style="width: 240px; height: 180px;" /></p>
<p><img alt="df01231d78aa426a8440e10119aad710" class="no-scaled-link" src="../../../../../_images/vb-patching.png" style="width: 240px; height: 180px;" /></p>
<p><span class="math notranslate nohighlight">\(P_+\)</span> is a central square centered at momentum <span class="math notranslate nohighlight">\((0,0)\)</span> and containing the nodal region; the complementary region <span class="math notranslate nohighlight">\(P_{-}\)</span> extends to the edge of the BZ and contains in particular the antinodal region and the <span class="math notranslate nohighlight">\((\pi,\pi)\)</span> momentum.</p>
<div class="nbinput docutils container">
<div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[1]:
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