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jenkins-TRIQS-triqs-unstable-1049 c504e379d01c850d10523567b6d2ac258a85c321
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Expand Up @@ -48,4 +48,4 @@ Parameters
Returns
^^^^^^^

True, if the original iterators are equal.
True, if the original iterator is equal to the iterator stored in the sentinel.
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Expand Up @@ -33,4 +33,4 @@ Documentation
Returns
^^^^^^^

Reference to the derived iterator after calling the derived iterator's `increment()` function.
Copy of the derived iterator before calling the derived iterator's `increment()` function.
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Expand Up @@ -48,4 +48,4 @@ Parameters
Returns
^^^^^^^

True, if all original iterators are equal.
True, if the first iterator, i.e. `std::get<0>(its)`, is equal to the iterator of the sentinel.
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Expand Up @@ -48,4 +48,4 @@ Parameters
Returns
^^^^^^^

True, if the original iterators are equal.
True, if the original iterator is equal to the iterator stored in the sentinel.
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Expand Up @@ -54,4 +54,4 @@ Parameters
Returns
^^^^^^^

std::string containing the result of the gather operation.
std::vector containing the result of the gather operation.
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Expand Up @@ -85,4 +85,4 @@ Parameters
Returns
^^^^^^^

The result of the reduction.
std::vector containing the result of each individual reduction.
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Expand Up @@ -41,4 +41,4 @@ Documentation
Returns
^^^^^^^

Reference to the storage container
Constant reference to the storage container
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Expand Up @@ -47,4 +47,4 @@ Parameters
Returns
^^^^^^^

Constant reference to the requested amplitude
Reference to the requested amplitude
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Expand Up @@ -47,4 +47,4 @@ Parameters
Returns
^^^^^^^

Constant reference to the requested amplitude
Reference to the requested amplitude
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Expand Up @@ -1838,7 +1838,7 @@ <h2>Parameters<a class="headerlink" href="#parameters" title="Link to this headi
</section>
<section id="returns">
<h2>Returns<a class="headerlink" href="#returns" title="Link to this heading"></a></h2>
<p>True, if the original iterators are equal.</p>
<p>True, if the original iterator is equal to the iterator stored in the sentinel.</p>
</section>
</section>

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Expand Up @@ -1820,7 +1820,7 @@
<p>Documentation</p>
<section id="returns">
<h2>Returns<a class="headerlink" href="#returns" title="Link to this heading"></a></h2>
<p>Reference to the derived iterator after calling the derived iterator’s <cite>increment()</cite> function.</p>
<p>Copy of the derived iterator before calling the derived iterator’s <cite>increment()</cite> function.</p>
</section>
</section>

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Expand Up @@ -1838,7 +1838,7 @@ <h2>Parameters<a class="headerlink" href="#parameters" title="Link to this headi
</section>
<section id="returns">
<h2>Returns<a class="headerlink" href="#returns" title="Link to this heading"></a></h2>
<p>True, if all original iterators are equal.</p>
<p>True, if the first iterator, i.e. <cite>std::get&lt;0&gt;(its)</cite>, is equal to the iterator of the sentinel.</p>
</section>
</section>

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Expand Up @@ -1838,7 +1838,7 @@ <h2>Parameters<a class="headerlink" href="#parameters" title="Link to this headi
</section>
<section id="returns">
<h2>Returns<a class="headerlink" href="#returns" title="Link to this heading"></a></h2>
<p>True, if the original iterators are equal.</p>
<p>True, if the original iterator is equal to the iterator stored in the sentinel.</p>
</section>
</section>

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2 changes: 1 addition & 1 deletion triqs/unstable/documentation/cpp_api/mpi/mpi_gather.html
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Expand Up @@ -1840,7 +1840,7 @@ <h2>Parameters<a class="headerlink" href="#parameters" title="Link to this headi
</section>
<section id="returns">
<h2>Returns<a class="headerlink" href="#returns" title="Link to this heading"></a></h2>
<p>std::string containing the result of the gather operation.</p>
<p>std::vector containing the result of the gather operation.</p>
</section>
</section>

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2 changes: 1 addition & 1 deletion triqs/unstable/documentation/cpp_api/mpi/mpi_reduce.html
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Expand Up @@ -1875,7 +1875,7 @@ <h2>Parameters<a class="headerlink" href="#parameters" title="Link to this headi
</section>
<section id="returns">
<h2>Returns<a class="headerlink" href="#returns" title="Link to this heading"></a></h2>
<p>The result of the reduction.</p>
<p>std::vector containing the result of each individual reduction.</p>
</section>
</section>

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Expand Up @@ -1824,7 +1824,7 @@
</div></blockquote>
<section id="returns">
<h2>Returns<a class="headerlink" href="#returns" title="Link to this heading"></a></h2>
<p>Reference to the storage container</p>
<p>Constant reference to the storage container</p>
</section>
</section>

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Expand Up @@ -1832,7 +1832,7 @@ <h2>Parameters<a class="headerlink" href="#parameters" title="Link to this headi
</section>
<section id="returns">
<h2>Returns<a class="headerlink" href="#returns" title="Link to this heading"></a></h2>
<p>Constant reference to the requested amplitude</p>
<p>Reference to the requested amplitude</p>
</section>
</section>

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Expand Up @@ -1832,7 +1832,7 @@ <h2>Parameters<a class="headerlink" href="#parameters" title="Link to this headi
</section>
<section id="returns">
<h2>Returns<a class="headerlink" href="#returns" title="Link to this heading"></a></h2>
<p>Constant reference to the requested amplitude</p>
<p>Reference to the requested amplitude</p>
</section>
</section>

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

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Expand Up @@ -2106,7 +2106,7 @@ <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="b2756e8c660449cca5bf4600a7cf591f" class="no-scaled-link" src="../../../../_images/selfcons.png" style="width: 40%;" /></p>
<p><img alt="7c460f5a47fc4af0970471337cc3f0dd" 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>
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Expand Up @@ -2070,7 +2070,7 @@
<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="fe5cfcaaf28d4b42b544cf6c7c812225" src="../../../../_images/dmft_bath_impurity.png" /></p>
<p><img alt="bbf3a8808691430ba0821fd6fd872d7b" 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}} \
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Expand Up @@ -2071,7 +2071,7 @@ <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="50890868baf640c78ea775185f3cef09" class="no-scaled-link" src="../../../../_images/vb-patching.png" style="width: 240px; height: 180px;" /></p>
<p><img alt="0ccfb327bcdb4b9d814ac964051d844f" 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]:
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Expand Up @@ -2117,7 +2117,7 @@ <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="3a373089fc454dcbb6911866bf1ba5b6" class="no-scaled-link" src="../../../../../_images/selfcons1.png" style="width: 40%;" /></p>
<p><img alt="4c174a9827324f58b744907230f5956a" 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>
Expand Down Expand Up @@ -2232,7 +2232,7 @@ <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="a10e424689dd4993a8d3d7fdf349b668" class="no-scaled-link" src="../../../../../_images/mott.png" style="width: 30%;" /></p>
<p><img alt="9514231f12b34d54bd8e6ffbf16d1b53" class="no-scaled-link" src="../../../../../_images/mott.png" style="width: 30%;" /></p>
</section>
</section>

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Expand Up @@ -2345,7 +2345,7 @@ <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="9d723e9562034c769c2efd80a67dd0ba" src="../../../../../_images/maxent_Aw.png" /></p>
<p><img alt="69af446490f949d1ba4edb8ab0e1cc6e" 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>
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Expand Up @@ -2075,7 +2075,7 @@ <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="bd3f2bff7ae04aa090e3fd02a9a3d154" class="no-scaled-link" src="../../../../../_images/vb-patching1.png" style="width: 240px; height: 180px;" /></p>
<p><img alt="f2663728d4c94f4390304ca4041217b5" 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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Expand Up @@ -2116,7 +2116,7 @@ <h2>Theory<a class="headerlink" href="#Theory" title="Link to this heading"><
<section id="Behaviour-of-U_{sp}-and-U_{ch}-vs. U">
<h2>Behaviour of <span class="math notranslate nohighlight">\(U_{sp}\)</span> and <span class="math notranslate nohighlight">\(U_{ch}\)</span> vs. <span class="math notranslate nohighlight">\(U\)</span><a class="headerlink" href="#Behaviour-of-U_{sp}-and-U_{ch}-vs. U" title="Link to this heading"></a></h2>
<p>Let’s study the behaviour of <span class="math notranslate nohighlight">\(U_{sp}\)</span> and <span class="math notranslate nohighlight">\(U_{ch}\)</span> as we vary <span class="math notranslate nohighlight">\(U\)</span>. This will require us to solve the TPSC equations described above. Our aim is to reproduce the results from <a class="reference external" href="https://jp1.journaldephysique.org/articles/jp1/abs/1997/11/jp1v7p1309/jp1v7p1309.html" rel="noopener noreferrer" target="_blank">[Vilk and Tremblay, J. Phys. I France 7 (1997) 1309-1368]</a> <a class="reference external" href="https://arxiv.org/abs/cond-mat/9702188v3" rel="noopener noreferrer" target="_blank">[arXiv version]</a> and the figure:</p>
<p><img alt="Drawing" src="../../../../_images/Fig2.png" /></p>
<p><img alt="Drawing" src="../../../../_images/Fig21.png" /></p>
<blockquote>
<div><p>Exercise 1:</p>
</div></blockquote>
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Expand Up @@ -2120,7 +2120,7 @@ <h2>Theory<a class="headerlink" href="#Theory" title="Link to this heading"><
<section id="Behaviour-of-U_{sp}-and-U_{ch}-vs. U">
<h2>Behaviour of <span class="math notranslate nohighlight">\(U_{sp}\)</span> and <span class="math notranslate nohighlight">\(U_{ch}\)</span> vs. <span class="math notranslate nohighlight">\(U\)</span><a class="headerlink" href="#Behaviour-of-U_{sp}-and-U_{ch}-vs. U" title="Link to this heading"></a></h2>
<p>Let’s study the behaviour of <span class="math notranslate nohighlight">\(U_{sp}\)</span> and <span class="math notranslate nohighlight">\(U_{ch}\)</span> as we vary <span class="math notranslate nohighlight">\(U\)</span>. This will require us to solve the TPSC equations described above. Our aim is to reproduce the results from <a class="reference external" href="https://jp1.journaldephysique.org/articles/jp1/abs/1997/11/jp1v7p1309/jp1v7p1309.html" rel="noopener noreferrer" target="_blank">[Vilk and Tremblay, J. Phys. I France 7 (1997) 1309-1368]</a> <a class="reference external" href="https://arxiv.org/abs/cond-mat/9702188v3" rel="noopener noreferrer" target="_blank">[arXiv version]</a> and the figure:</p>
<p><img alt="Drawing" src="../../../../../_images/Fig21.png" /></p>
<p><img alt="Drawing" src="../../../../../_images/Fig2.png" /></p>
<blockquote>
<div><p>Exercise 1:</p>
</div></blockquote>
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