diff --git a/_sass/thesis.scss b/_sass/thesis.scss index 5557bc3..5fc5322 100644 --- a/_sass/thesis.scss +++ b/_sass/thesis.scss @@ -84,4 +84,9 @@ nav.overall-table-of-contents > ul { list-style: none; margin-top: 1em; } +} + +// Page header +div#page-header { + p { margin-block-end: 0px;} } \ No newline at end of file diff --git a/_thesis/1_Introduction/1_Intro.html b/_thesis/1_Introduction/1_Intro.html index 8987746..a6efefb 100644 --- a/_thesis/1_Introduction/1_Intro.html +++ b/_thesis/1_Introduction/1_Intro.html @@ -61,6 +61,10 @@ id="toc-quantum-spin-liquids">Quantum Spin Liquids --> +
+

1 Introduction

+
+

Interacting Quantum Many Body Systems

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 Falikov-Kimball Model in one dimension while Chapter 4 focusses on the Amorphous Kitaev Model.

+

Next Chapter: 2 +Background

Bibliography

diff --git a/_thesis/2_Background/2.1_FK_Model.html b/_thesis/2_Background/2.1_FK_Model.html index e479f73..e2c5928 100644 --- a/_thesis/2_Background/2.1_FK_Model.html +++ b/_thesis/2_Background/2.1_FK_Model.html @@ -64,6 +64,10 @@ id="toc-long-ranged-ising-model">Long Ranged Ising model --> +
+

2 Background

+
+

The Falikov Kimball Model

@@ -415,6 +419,9 @@ j|^{-\alpha} S_i S_j\) as the exponent of the interaction \(\alpha\) is varied. +

Next Section: The +Kitaev Honeycomb Model

diff --git a/_thesis/2_Background/2.2_HKM_Model.html b/_thesis/2_Background/2.2_HKM_Model.html index 37043a9..f510c47 100644 --- a/_thesis/2_Background/2.2_HKM_Model.html +++ b/_thesis/2_Background/2.2_HKM_Model.html @@ -74,6 +74,10 @@ Diagram --> +
+

2 Background

+
+

The Kitaev Honeycomb Model

papers Jos on dynamics @@ -136,6 +140,9 @@ role="doc-biblioref">1]

Phase Diagram

+

Next Section: Disorder +and Localisation

diff --git a/_thesis/2_Background/2.3_Disorder.html b/_thesis/2_Background/2.3_Disorder.html index af43638..8b2820e 100644 --- a/_thesis/2_Background/2.3_Disorder.html +++ b/_thesis/2_Background/2.3_Disorder.html @@ -70,6 +70,10 @@ id="toc-amorphous-magnetism">Amorphous Magnetism --> +
+

2 Background

+
+

Disorder and Localisation

-link to the FK model

-link to the Kitaev Model

-link to the physics of amorphous systems

+

Next Chapter: 3 +The Long Range Falikov-Kimball Model

diff --git a/_thesis/3_Long_Range_Falikov_Kimball/3.1_LRFK_Model.html b/_thesis/3_Long_Range_Falikov_Kimball/3.1_LRFK_Model.html index 8c71301..46036c8 100644 --- a/_thesis/3_Long_Range_Falikov_Kimball/3.1_LRFK_Model.html +++ b/_thesis/3_Long_Range_Falikov_Kimball/3.1_LRFK_Model.html @@ -48,6 +48,10 @@ image: --> +
+

3 The Long Range Falikov-Kimball Model

+
+

This chapter expands on work presented in

  [ [30]. We only consider even system sizes given that odd system sizes are not commensurate with a CDW state.

+

Next Section: Methods

Bibliography

diff --git a/_thesis/3_Long_Range_Falikov_Kimball/3.3_LRFK_Results.html b/_thesis/3_Long_Range_Falikov_Kimball/3.3_LRFK_Results.html index bf28dc5..438c43f 100644 --- a/_thesis/3_Long_Range_Falikov_Kimball/3.3_LRFK_Results.html +++ b/_thesis/3_Long_Range_Falikov_Kimball/3.3_LRFK_Results.html @@ -64,6 +64,10 @@ Conclusion --> +
+

3 The Long Range Falikov-Kimball Model

+
+

Results

@@ -465,6 +469,9 @@ H_{\mathrm{DM}} = & \;U \sum_{i} (-1)^i \; d_i \;(c^\dag_{i}c_{i} - \nonumber\end{aligned}\]

+

Next Chapter: 4 +The Amorphous Kitaev Model

Bibliography

diff --git a/_thesis/4_Amorphous_Kitaev_Model/4.1.2_AMK_Model.html b/_thesis/4_Amorphous_Kitaev_Model/4.1.2_AMK_Model.html index d558ae8..4887d94 100644 --- a/_thesis/4_Amorphous_Kitaev_Model/4.1.2_AMK_Model.html +++ b/_thesis/4_Amorphous_Kitaev_Model/4.1.2_AMK_Model.html @@ -137,6 +137,10 @@ Statistics --> +
+

4 The Amorphous Kitaev Model

+
+

Gauge Fields

The bond operators \(u_{ij}\) are @@ -1065,6 +1069,9 @@ href="#ref-hastingsDynamicallyGeneratedLogical2021" role="doc-biblioref">16,kitaevFaulttolerantQuantumComputation2003?].

+

Next Section: The +Model

diff --git a/_thesis/4_Amorphous_Kitaev_Model/4.1_AMK_Model.html b/_thesis/4_Amorphous_Kitaev_Model/4.1_AMK_Model.html index 8b67fd5..f886cf0 100644 --- a/_thesis/4_Amorphous_Kitaev_Model/4.1_AMK_Model.html +++ b/_thesis/4_Amorphous_Kitaev_Model/4.1_AMK_Model.html @@ -105,6 +105,10 @@ id="toc-open-boundary-conditions">Open boundary conditions --> +
+

4 The Amorphous Kitaev Model

+
+

Contributions

The material in this chapter expands on work presented in

  anyway, an arbitrary pairing of the unpaired \(b^\alpha\) operators could be performed. </i,j></i,j>

+

Next Section: Methods

diff --git a/_thesis/4_Amorphous_Kitaev_Model/4.2_AMK_Methods.html b/_thesis/4_Amorphous_Kitaev_Model/4.2_AMK_Methods.html index 018ebc4..e903f18 100644 --- a/_thesis/4_Amorphous_Kitaev_Model/4.2_AMK_Methods.html +++ b/_thesis/4_Amorphous_Kitaev_Model/4.2_AMK_Methods.html @@ -95,6 +95,10 @@ Markers --> +
+

4 The Amorphous Kitaev Model

+
+
@@ -536,6 +540,8 @@ system.

Expand on definition here

Discuss link between Chern number and Anyonic Statistics

+

Next Section: Results

diff --git a/_thesis/4_Amorphous_Kitaev_Model/4.3_AMK_Results.html b/_thesis/4_Amorphous_Kitaev_Model/4.3_AMK_Results.html index 3736b56..9e7afb0 100644 --- a/_thesis/4_Amorphous_Kitaev_Model/4.3_AMK_Results.html +++ b/_thesis/4_Amorphous_Kitaev_Model/4.3_AMK_Results.html @@ -103,6 +103,10 @@ id="toc-amk-discussion">Discussion --> +
+

4 The Amorphous Kitaev Model

+
+

Results

@@ -661,6 +665,8 @@ href="#ref-Wu2009" role="doc-biblioref">47]

quantum many body phases albeit material candidates aplenty. We expect our exact chiral amorphous spin liquid to find many generalisation to realistic amorphous quantum magnets and beyond.

+

Next Chapter: 5 Conclusion

diff --git a/_thesis/5_Conclusion/5_Conclusion.html b/_thesis/5_Conclusion/5_Conclusion.html index 7c468cb..d806d0a 100644 --- a/_thesis/5_Conclusion/5_Conclusion.html +++ b/_thesis/5_Conclusion/5_Conclusion.html @@ -48,11 +48,17 @@ image: --> +
+

5 Conclusion

+
+

Discussion

Outlook

+

Next Chapter: Appendices

diff --git a/_thesis/6_Appendices/A.1_Particle_Hole_Symmetry.html b/_thesis/6_Appendices/A.1_Particle_Hole_Symmetry.html index c342c80..48ed5ee 100644 --- a/_thesis/6_Appendices/A.1_Particle_Hole_Symmetry.html +++ b/_thesis/6_Appendices/A.1_Particle_Hole_Symmetry.html @@ -50,6 +50,10 @@ id="toc-particle-hole-symmetry">Particle-Hole Symmetry --> +
+

Appendices

+
+

Particle-Hole Symmetry

The Hubbard and FK models on a bipartite lattice have particle-hole @@ -108,6 +112,9 @@ class="math inline">\(\mu = 0\) and so must all the observables, hence half filling \(\rho = 1\) occurs here. This symmetry and known observable acts as a useful test for the numerical calculations.

+

Next Section: Applying +MCMC to the FK model

Bibliography

diff --git a/_thesis/6_Appendices/A.2_Markov_Chain_Monte_Carlo.html b/_thesis/6_Appendices/A.2_Markov_Chain_Monte_Carlo.html index 8b277a1..a3c9d29 100644 --- a/_thesis/6_Appendices/A.2_Markov_Chain_Monte_Carlo.html +++ b/_thesis/6_Appendices/A.2_Markov_Chain_Monte_Carlo.html @@ -58,6 +58,10 @@ model --> +
+

Appendices

+
+

Markov Chain Monte Carlo

@@ -137,6 +141,9 @@ walk progresses.

+

Next Section: Lattice +Generation

diff --git a/_thesis/6_Appendices/A.3_Lattice_Generation.html b/_thesis/6_Appendices/A.3_Lattice_Generation.html index 1ceefc7..704c3aa 100644 --- a/_thesis/6_Appendices/A.3_Lattice_Generation.html +++ b/_thesis/6_Appendices/A.3_Lattice_Generation.html @@ -48,10 +48,17 @@ Generation --> +
+

Appendices

+
+

Lattice Generation

+

Next Section: Lattice +Colouring

diff --git a/_thesis/6_Appendices/A.4_Lattice_Colouring.html b/_thesis/6_Appendices/A.4_Lattice_Colouring.html index 62478c3..2f5a997 100644 --- a/_thesis/6_Appendices/A.4_Lattice_Colouring.html +++ b/_thesis/6_Appendices/A.4_Lattice_Colouring.html @@ -48,6 +48,10 @@ Colouring --> +
+

Appendices

+
+

Lattice Colouring