add extra info for each page

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Tom Hodson 2022-08-27 13:03:20 +02:00
parent 941b83e767
commit c23fcc5acb
18 changed files with 111 additions and 5 deletions

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@ -84,4 +84,9 @@ nav.overall-table-of-contents > ul {
list-style: none; list-style: none;
margin-top: 1em; margin-top: 1em;
} }
}
// Page header
div#page-header {
p { margin-block-end: 0px;}
} }

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@ -61,6 +61,10 @@ id="toc-quantum-spin-liquids">Quantum Spin Liquids</a></li>
--> -->
<!-- Main Page Body --> <!-- Main Page Body -->
<div id="page-header">
<p>1 Introduction</p>
<hr />
</div>
<section id="interacting-quantum-many-body-systems" class="level1"> <section id="interacting-quantum-many-body-systems" class="level1">
<h1>Interacting Quantum Many Body Systems</h1> <h1>Interacting Quantum Many Body Systems</h1>
<p>When you take many objects and let them interact together, it is <p>When you take many objects and let them interact together, it is
@ -591,6 +595,9 @@ to the Falikov-Kimball Model, the Kitaev Honeycomb Model, disorder and
localisation. Then Chapter 3 introduces and studies the Long Range localisation. Then Chapter 3 introduces and studies the Long Range
Falikov-Kimball Model in one dimension while Chapter 4 focusses on the Falikov-Kimball Model in one dimension while Chapter 4 focusses on the
Amorphous Kitaev Model.</p> Amorphous Kitaev Model.</p>
<p>Next Chapter: <a
href="../2_Background/2.1_FK_Model.html#the-falikov-kimball-model">2
Background</a></p>
</section> </section>
<section id="bibliography" class="level1 unnumbered"> <section id="bibliography" class="level1 unnumbered">
<h1 class="unnumbered">Bibliography</h1> <h1 class="unnumbered">Bibliography</h1>

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@ -64,6 +64,10 @@ id="toc-long-ranged-ising-model">Long Ranged Ising model</a></li>
--> -->
<!-- Main Page Body --> <!-- Main Page Body -->
<div id="page-header">
<p>2 Background</p>
<hr />
</div>
<section id="the-falikov-kimball-model" class="level1"> <section id="the-falikov-kimball-model" class="level1">
<h1>The Falikov Kimball Model</h1> <h1>The Falikov Kimball Model</h1>
<section id="the-model" class="level2"> <section id="the-model" class="level2">
@ -415,6 +419,9 @@ j|^{-\alpha} S_i S_j\)</span> as the exponent of the interaction <span
class="math inline">\(\alpha\)</span> is varied.</figcaption> class="math inline">\(\alpha\)</span> is varied.</figcaption>
</figure> </figure>
</div> </div>
<p>Next Section: <a
href="../2_Background/2.2_HKM_Model.html#the-kitaev-honeycomb-model">The
Kitaev Honeycomb Model</a></p>
</section> </section>
</section> </section>
<section id="bibliography" class="level1 unnumbered"> <section id="bibliography" class="level1 unnumbered">

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@ -74,6 +74,10 @@ Diagram</a></li>
--> -->
<!-- Main Page Body --> <!-- Main Page Body -->
<div id="page-header">
<p>2 Background</p>
<hr />
</div>
<section id="the-kitaev-honeycomb-model" class="level1"> <section id="the-kitaev-honeycomb-model" class="level1">
<h1>The Kitaev Honeycomb Model</h1> <h1>The Kitaev Honeycomb Model</h1>
<p><strong>papers</strong> Jos on dynamics <p><strong>papers</strong> Jos on dynamics
@ -136,6 +140,9 @@ role="doc-biblioref">1</a>]</span></li>
<h2>Phase Diagram</h2> <h2>Phase Diagram</h2>
<div class="sourceCode" id="cb1"><pre <div class="sourceCode" id="cb1"><pre
class="sourceCode python"><code class="sourceCode python"></code></pre></div> class="sourceCode python"><code class="sourceCode python"></code></pre></div>
<p>Next Section: <a
href="../2_Background/2.3_Disorder.html#bg-disorder-and-localisation">Disorder
and Localisation</a></p>
</section> </section>
</section> </section>
<section id="bibliography" class="level1 unnumbered"> <section id="bibliography" class="level1 unnumbered">

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@ -70,6 +70,10 @@ id="toc-amorphous-magnetism">Amorphous Magnetism</a></li>
--> -->
<!-- Main Page Body --> <!-- Main Page Body -->
<div id="page-header">
<p>2 Background</p>
<hr />
</div>
<section id="bg-disorder-and-localisation" class="level1"> <section id="bg-disorder-and-localisation" class="level1">
<h1>Disorder and Localisation</h1> <h1>Disorder and Localisation</h1>
<section id="localisation-anderson-many-body-and-disorder-free" <section id="localisation-anderson-many-body-and-disorder-free"
@ -169,6 +173,9 @@ timescales to the infinite limit.</p>
<p>-link to the FK model</p> <p>-link to the FK model</p>
<p>-link to the Kitaev Model</p> <p>-link to the Kitaev Model</p>
<p>-link to the physics of amorphous systems</p> <p>-link to the physics of amorphous systems</p>
<p>Next Chapter: <a
href="../3_Long_Range_Falikov_Kimball/3.1_LRFK_Model.html#fk-model">3
The Long Range Falikov-Kimball Model</a></p>
</section> </section>
</section> </section>
<section id="bibliography" class="level1 unnumbered"> <section id="bibliography" class="level1 unnumbered">

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@ -48,6 +48,10 @@ image:
--> -->
<!-- Main Page Body --> <!-- Main Page Body -->
<div id="page-header">
<p>3 The Long Range Falikov-Kimball Model</p>
<hr />
</div>
<p>This chapter expands on work presented in</p> <p>This chapter expands on work presented in</p>
<p> <span class="citation" <p> <span class="citation"
data-cites="hodsonOnedimensionalLongrangeFalikovKimball2021"> [<a data-cites="hodsonOnedimensionalLongrangeFalikovKimball2021"> [<a
@ -267,6 +271,8 @@ data-cites="fukuiOrderNClusterMonte2009"> [<a
href="#ref-fukuiOrderNClusterMonte2009" href="#ref-fukuiOrderNClusterMonte2009"
role="doc-biblioref">30</a>]</span>. We only consider even system sizes role="doc-biblioref">30</a>]</span>. We only consider even system sizes
given that odd system sizes are not commensurate with a CDW state.</p> given that odd system sizes are not commensurate with a CDW state.</p>
<p>Next Section: <a
href="../3_Long_Range_Falikov_Kimball/3.2_LRFK_Methods.html#fk-methods">Methods</a></p>
</section> </section>
<section id="bibliography" class="level1 unnumbered"> <section id="bibliography" class="level1 unnumbered">
<h1 class="unnumbered">Bibliography</h1> <h1 class="unnumbered">Bibliography</h1>

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@ -64,6 +64,10 @@ Conclusion</a></li>
--> -->
<!-- Main Page Body --> <!-- Main Page Body -->
<div id="page-header">
<p>3 The Long Range Falikov-Kimball Model</p>
<hr />
</div>
<section id="fk-results" class="level1"> <section id="fk-results" class="level1">
<h1>Results</h1> <h1>Results</h1>
<div id="fig:phase_diagram" class="fignos"> <div id="fig:phase_diagram" class="fignos">
@ -465,6 +469,9 @@ H_{\mathrm{DM}} = &amp; \;U \sum_{i} (-1)^i \; d_i \;(c^\dag_{i}c_{i} -
\nonumber\end{aligned}\]</span></p> \nonumber\end{aligned}\]</span></p>
<div class="sourceCode" id="cb1"><pre <div class="sourceCode" id="cb1"><pre
class="sourceCode python"><code class="sourceCode python"></code></pre></div> class="sourceCode python"><code class="sourceCode python"></code></pre></div>
<p>Next Chapter: <a
href="../4_Amorphous_Kitaev_Model/4.1.2_AMK_Model.html#vortices-and-their-movements">4
The Amorphous Kitaev Model</a></p>
</section> </section>
<section id="bibliography" class="level1 unnumbered"> <section id="bibliography" class="level1 unnumbered">
<h1 class="unnumbered">Bibliography</h1> <h1 class="unnumbered">Bibliography</h1>

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@ -137,6 +137,10 @@ Statistics</a></li>
--> -->
<!-- Main Page Body --> <!-- Main Page Body -->
<div id="page-header">
<p>4 The Amorphous Kitaev Model</p>
<hr />
</div>
<section id="gauge-fields" class="level2"> <section id="gauge-fields" class="level2">
<h2>Gauge Fields</h2> <h2>Gauge Fields</h2>
<p>The bond operators <span class="math inline">\(u_{ij}\)</span> are <p>The bond operators <span class="math inline">\(u_{ij}\)</span> are
@ -1065,6 +1069,9 @@ href="#ref-hastingsDynamicallyGeneratedLogical2021"
role="doc-biblioref">16</a>,<a role="doc-biblioref">16</a>,<a
href="#ref-kitaevFaulttolerantQuantumComputation2003" href="#ref-kitaevFaulttolerantQuantumComputation2003"
role="doc-biblioref"><strong>kitaevFaulttolerantQuantumComputation2003?</strong></a>]</span>.</p> role="doc-biblioref"><strong>kitaevFaulttolerantQuantumComputation2003?</strong></a>]</span>.</p>
<p>Next Section: <a
href="../4_Amorphous_Kitaev_Model/4.1_AMK_Model.html#amk-Model">The
Model</a></p>
</section> </section>
</section> </section>
<section id="bibliography" class="level1 unnumbered"> <section id="bibliography" class="level1 unnumbered">

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@ -105,6 +105,10 @@ id="toc-open-boundary-conditions">Open boundary conditions</a></li>
--> -->
<!-- Main Page Body --> <!-- Main Page Body -->
<div id="page-header">
<p>4 The Amorphous Kitaev Model</p>
<hr />
</div>
<p><strong>Contributions</strong></p> <p><strong>Contributions</strong></p>
<p>The material in this chapter expands on work presented in</p> <p>The material in this chapter expands on work presented in</p>
<p> <span class="citation" <p> <span class="citation"
@ -764,6 +768,8 @@ which we set to 1 when calculating the projector.</p>
anyway, an arbitrary pairing of the unpaired <span anyway, an arbitrary pairing of the unpaired <span
class="math inline">\(b^\alpha\)</span> operators could be performed. class="math inline">\(b^\alpha\)</span> operators could be performed.
&lt;/i,j&gt;&lt;/i,j&gt;</p> &lt;/i,j&gt;&lt;/i,j&gt;</p>
<p>Next Section: <a
href="../4_Amorphous_Kitaev_Model/4.2_AMK_Methods.html#amk-methods">Methods</a></p>
</section> </section>
</section> </section>
</section> </section>

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@ -95,6 +95,10 @@ Markers</a></li>
--> -->
<!-- Main Page Body --> <!-- Main Page Body -->
<div id="page-header">
<p>4 The Amorphous Kitaev Model</p>
<hr />
</div>
<div class="sourceCode" id="cb1"><pre <div class="sourceCode" id="cb1"><pre
class="sourceCode python"><code class="sourceCode python"></code></pre></div> class="sourceCode python"><code class="sourceCode python"></code></pre></div>
<section id="amk-methods" class="level1"> <section id="amk-methods" class="level1">
@ -536,6 +540,8 @@ system.</p>
<p><strong>Expand on definition here</strong></p> <p><strong>Expand on definition here</strong></p>
<p><strong>Discuss link between Chern number and Anyonic <p><strong>Discuss link between Chern number and Anyonic
Statistics</strong></p> Statistics</strong></p>
<p>Next Section: <a
href="../4_Amorphous_Kitaev_Model/4.3_AMK_Results.html#amk-results">Results</a></p>
</section> </section>
</section> </section>
<section id="bibliography" class="level1 unnumbered"> <section id="bibliography" class="level1 unnumbered">

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@ -103,6 +103,10 @@ id="toc-amk-discussion">Discussion</a></li>
--> -->
<!-- Main Page Body --> <!-- Main Page Body -->
<div id="page-header">
<p>4 The Amorphous Kitaev Model</p>
<hr />
</div>
<section id="amk-results" class="level1"> <section id="amk-results" class="level1">
<h1>Results</h1> <h1>Results</h1>
<section id="the-ground-state-flux-sector" class="level2"> <section id="the-ground-state-flux-sector" class="level2">
@ -661,6 +665,8 @@ href="#ref-Wu2009" role="doc-biblioref">47</a>]</span></p>
quantum many body phases albeit material candidates aplenty. We expect quantum many body phases albeit material candidates aplenty. We expect
our exact chiral amorphous spin liquid to find many generalisation to our exact chiral amorphous spin liquid to find many generalisation to
realistic amorphous quantum magnets and beyond.</p> realistic amorphous quantum magnets and beyond.</p>
<p>Next Chapter: <a
href="../5_Conclusion/5_Conclusion.html#discussion">5 Conclusion</a></p>
</section> </section>
</section> </section>
<section id="bibliography" class="level1 unnumbered"> <section id="bibliography" class="level1 unnumbered">

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@ -48,11 +48,17 @@ image:
--> -->
<!-- Main Page Body --> <!-- Main Page Body -->
<div id="page-header">
<p>5 Conclusion</p>
<hr />
</div>
<section id="discussion" class="level2"> <section id="discussion" class="level2">
<h2>Discussion</h2> <h2>Discussion</h2>
</section> </section>
<section id="outlook" class="level2"> <section id="outlook" class="level2">
<h2>Outlook</h2> <h2>Outlook</h2>
<p>Next Chapter: <a
href="../6_Appendices/A.1_Particle_Hole_Symmetry.html#particle-hole-symmetry">Appendices</a></p>
</section> </section>

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@ -50,6 +50,10 @@ id="toc-particle-hole-symmetry">Particle-Hole Symmetry</a></li>
--> -->
<!-- Main Page Body --> <!-- Main Page Body -->
<div id="page-header">
<p>Appendices</p>
<hr />
</div>
<section id="particle-hole-symmetry" class="level1"> <section id="particle-hole-symmetry" class="level1">
<h1>Particle-Hole Symmetry</h1> <h1>Particle-Hole Symmetry</h1>
<p>The Hubbard and FK models on a bipartite lattice have particle-hole <p>The Hubbard and FK models on a bipartite lattice have particle-hole
@ -108,6 +112,9 @@ class="math inline">\(\mu = 0\)</span> and so must all the observables,
hence half filling <span class="math inline">\(\rho = 1\)</span> occurs hence half filling <span class="math inline">\(\rho = 1\)</span> occurs
here. This symmetry and known observable acts as a useful test for the here. This symmetry and known observable acts as a useful test for the
numerical calculations.</p> numerical calculations.</p>
<p>Next Section: <a
href="../6_Appendices/A.2_Markov_Chain_Monte_Carlo.html#applying-mcmc-to-the-fk-model">Applying
MCMC to the FK model</a></p>
</section> </section>
<section id="bibliography" class="level1 unnumbered"> <section id="bibliography" class="level1 unnumbered">
<h1 class="unnumbered">Bibliography</h1> <h1 class="unnumbered">Bibliography</h1>

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@ -58,6 +58,10 @@ model</a></li>
--> -->
<!-- Main Page Body --> <!-- Main Page Body -->
<div id="page-header">
<p>Appendices</p>
<hr />
</div>
<section id="markov-chain-monte-carlo" class="level1"> <section id="markov-chain-monte-carlo" class="level1">
<h1>Markov Chain Monte Carlo</h1> <h1>Markov Chain Monte Carlo</h1>
<section id="applying-mcmc-to-the-fk-model" class="level2"> <section id="applying-mcmc-to-the-fk-model" class="level2">
@ -137,6 +141,9 @@ walk progresses.</p>
<div class="sourceCode" id="cb1"><pre <div class="sourceCode" id="cb1"><pre
class="sourceCode python"><code class="sourceCode python"></code></pre></div> class="sourceCode python"><code class="sourceCode python"></code></pre></div>
<p></ij></ij></p> <p></ij></ij></p>
<p>Next Section: <a
href="../6_Appendices/A.3_Lattice_Generation.html#lattice-generation">Lattice
Generation</a></p>
</section> </section>
</section> </section>

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@ -48,10 +48,17 @@ Generation</a></li>
--> -->
<!-- Main Page Body --> <!-- Main Page Body -->
<div id="page-header">
<p>Appendices</p>
<hr />
</div>
<section id="lattice-generation" class="level1"> <section id="lattice-generation" class="level1">
<h1>Lattice Generation</h1> <h1>Lattice Generation</h1>
<div class="sourceCode" id="cb1"><pre <div class="sourceCode" id="cb1"><pre
class="sourceCode python"><code class="sourceCode python"></code></pre></div> class="sourceCode python"><code class="sourceCode python"></code></pre></div>
<p>Next Section: <a
href="../6_Appendices/A.4_Lattice_Colouring.html#lattice-colouring">Lattice
Colouring</a></p>
</section> </section>

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@ -48,6 +48,10 @@ Colouring</a></li>
--> -->
<!-- Main Page Body --> <!-- Main Page Body -->
<div id="page-header">
<p>Appendices</p>
<hr />
</div>
<section id="lattice-colouring" class="level1"> <section id="lattice-colouring" class="level1">
<h1>Lattice Colouring</h1> <h1>Lattice Colouring</h1>
<div class="sourceCode" id="cb1"><pre <div class="sourceCode" id="cb1"><pre

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@ -48,6 +48,10 @@ Projector</a></li>
--> -->
<!-- Main Page Body --> <!-- Main Page Body -->
<div id="page-header">
<p>Appendices</p>
<hr />
</div>
<section id="app-the-projector" class="level1"> <section id="app-the-projector" class="level1">
<h1>The Projector</h1> <h1>The Projector</h1>
</section> </section>

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@ -1,31 +1,31 @@
<ul> <ul>
<li><a href="./1_Introduction/1_Intro.html#interacting-quantum-many-body-systems">Introduction</a></li> <li><a href="./1_Introduction/1_Intro.html#interacting-quantum-many-body-systems">1 Introduction</a></li>
<ul> <ul>
<li><a href="./1_Introduction/1_Intro.html#interacting-quantum-many-body-systems">Interacting Quantum Many Body Systems</a></li> <li><a href="./1_Introduction/1_Intro.html#interacting-quantum-many-body-systems">Interacting Quantum Many Body Systems</a></li>
<li><a href="./1_Introduction/1_Intro.html#mott-insulators">Mott Insulators</a></li> <li><a href="./1_Introduction/1_Intro.html#mott-insulators">Mott Insulators</a></li>
<li><a href="./1_Introduction/1_Intro.html#quantum-spin-liquids">Quantum Spin Liquids</a></li> <li><a href="./1_Introduction/1_Intro.html#quantum-spin-liquids">Quantum Spin Liquids</a></li>
</ul> </ul>
<li><a href="./2_Background/2.1_FK_Model.html#the-falikov-kimball-model">Background</a></li> <li><a href="./2_Background/2.1_FK_Model.html#the-falikov-kimball-model">2 Background</a></li>
<ul> <ul>
<li><a href="./2_Background/2.1_FK_Model.html#the-falikov-kimball-model">The Falikov Kimball Model</a></li> <li><a href="./2_Background/2.1_FK_Model.html#the-falikov-kimball-model">The Falikov Kimball Model</a></li>
<li><a href="./2_Background/2.2_HKM_Model.html#the-kitaev-honeycomb-model">The Kitaev Honeycomb Model</a></li> <li><a href="./2_Background/2.2_HKM_Model.html#the-kitaev-honeycomb-model">The Kitaev Honeycomb Model</a></li>
<li><a href="./2_Background/2.3_Disorder.html#disorder-and-localisation">Disorder and Localisation</a></li> <li><a href="./2_Background/2.3_Disorder.html#disorder-and-localisation">Disorder and Localisation</a></li>
</ul> </ul>
<li><a href="./3_Long_Range_Falikov_Kimball/3.1_LRFK_Model.html#the-model">Chapter 3: The Long Range Falikov-Kimball Model</a></li> <li><a href="./3_Long_Range_Falikov_Kimball/3.1_LRFK_Model.html#the-model">3 The Long Range Falikov-Kimball Model</a></li>
<ul> <ul>
<li><a href="./3_Long_Range_Falikov_Kimball/3.1_LRFK_Model.html#the-model">The Model</a></li> <li><a href="./3_Long_Range_Falikov_Kimball/3.1_LRFK_Model.html#the-model">The Model</a></li>
<li><a href="./3_Long_Range_Falikov_Kimball/3.2_LRFK_Methods.html#methods">Methods</a></li> <li><a href="./3_Long_Range_Falikov_Kimball/3.2_LRFK_Methods.html#methods">Methods</a></li>
<li><a href="./3_Long_Range_Falikov_Kimball/3.3_LRFK_Results.html#results">Results</a></li> <li><a href="./3_Long_Range_Falikov_Kimball/3.3_LRFK_Results.html#results">Results</a></li>
<li><a href="./3_Long_Range_Falikov_Kimball/3.3_LRFK_Results.html#discussion-and-conclusion">Discussion and Conclusion</a></li> <li><a href="./3_Long_Range_Falikov_Kimball/3.3_LRFK_Results.html#discussion-and-conclusion">Discussion and Conclusion</a></li>
</ul> </ul>
<li><a href="./4_Amorphous_Kitaev_Model/4.1.2_AMK_Model.html#gauge-fields">Chapter 4: The Amorphous Kitaev Model</a></li> <li><a href="./4_Amorphous_Kitaev_Model/4.1.2_AMK_Model.html#gauge-fields">4 The Amorphous Kitaev Model</a></li>
<ul> <ul>
<li><a href="./4_Amorphous_Kitaev_Model/4.1_AMK_Model.html#the-model">The Model</a></li> <li><a href="./4_Amorphous_Kitaev_Model/4.1_AMK_Model.html#the-model">The Model</a></li>
<li><a href="./4_Amorphous_Kitaev_Model/4.2_AMK_Methods.html#methods">Methods</a></li> <li><a href="./4_Amorphous_Kitaev_Model/4.2_AMK_Methods.html#methods">Methods</a></li>
<li><a href="./4_Amorphous_Kitaev_Model/4.3_AMK_Results.html#results">Results</a></li> <li><a href="./4_Amorphous_Kitaev_Model/4.3_AMK_Results.html#results">Results</a></li>
<li><a href="./4_Amorphous_Kitaev_Model/4.3_AMK_Results.html#discussion-and-conclusion">Discussion and Conclusion</a></li> <li><a href="./4_Amorphous_Kitaev_Model/4.3_AMK_Results.html#discussion-and-conclusion">Discussion and Conclusion</a></li>
</ul> </ul>
<li><a href="./5_Conclusion/5_Conclusion.html#discussion">Conclusion</a></li> <li><a href="./5_Conclusion/5_Conclusion.html#discussion">5 Conclusion</a></li>
<li><a href="./6_Appendices/A.1_Particle_Hole_Symmetry.html#particle-hole-symmetry">Appendices</a></li> <li><a href="./6_Appendices/A.1_Particle_Hole_Symmetry.html#particle-hole-symmetry">Appendices</a></li>
<ul> <ul>
<li><a href="./6_Appendices/A.1_Particle_Hole_Symmetry.html#particle-hole-symmetry">Particle-Hole Symmetry</a></li> <li><a href="./6_Appendices/A.1_Particle_Hole_Symmetry.html#particle-hole-symmetry">Particle-Hole Symmetry</a></li>