updates!

Gemfile.lock

@@ -1,8 +1,8 @@
 GEM
   remote: https://rubygems.org/
   specs:
-    addressable (2.8.0)
-      public_suffix (>= 2.0.2, < 5.0)
+    addressable (2.8.1)
+      public_suffix (>= 2.0.2, < 6.0)
     colorator (1.1.0)
     concurrent-ruby (1.1.10)
     em-websocket (0.5.3)
@@ -12,24 +12,25 @@ GEM
     ffi (1.15.5)
     forwardable-extended (2.6.0)
     http_parser.rb (0.8.0)
-    i18n (1.10.0)
+    i18n (1.12.0)
       concurrent-ruby (~> 1.0)
-    jekyll (4.2.2)
+    jekyll (4.3.1)
       addressable (~> 2.4)
       colorator (~> 1.0)
       em-websocket (~> 0.5)
       i18n (~> 1.0)
-      jekyll-sass-converter (~> 2.0)
+      jekyll-sass-converter (>= 2.0, < 4.0)
       jekyll-watch (~> 2.0)
-      kramdown (~> 2.3)
+      kramdown (~> 2.3, >= 2.3.1)
       kramdown-parser-gfm (~> 1.0)
       liquid (~> 4.0)
-      mercenary (~> 0.4.0)
+      mercenary (>= 0.3.6, < 0.5)
       pathutil (~> 0.9)
-      rouge (~> 3.0)
+      rouge (>= 3.0, < 5.0)
       safe_yaml (~> 1.0)
-      terminal-table (~> 2.0)
-    jekyll-feed (0.16.0)
+      terminal-table (>= 1.8, < 4.0)
+      webrick (~> 1.7)
+    jekyll-feed (0.17.0)
       jekyll (>= 3.7, < 5.0)
     jekyll-redirect-from (0.16.0)
       jekyll (>= 3.3, < 5.0)
@@ -48,22 +49,22 @@ GEM
     mercenary (0.4.0)
     pathutil (0.16.2)
       forwardable-extended (~> 2.6)
-    public_suffix (4.0.7)
-    rb-fsevent (0.11.1)
+    public_suffix (5.0.0)
+    rb-fsevent (0.11.2)
     rb-inotify (0.10.1)
       ffi (~> 1.0)
     rexml (3.2.5)
-    rouge (3.29.0)
+    rouge (4.0.0)
     safe_yaml (1.0.5)
     sassc (2.4.0)
       ffi (~> 1.9)
-    terminal-table (2.0.0)
-      unicode-display_width (~> 1.1, >= 1.1.1)
-    unicode-display_width (1.8.0)
+    terminal-table (3.0.2)
+      unicode-display_width (>= 1.1.1, < 3)
+    unicode-display_width (2.3.0)
     webrick (1.7.0)
 
 PLATFORMS
-  x86_64-darwin-20
+  x86_64-darwin-21
 
 DEPENDENCIES
   jekyll

README.md

@@ -1,5 +1,8 @@
 Generates my personal website. I copied (rather than forked to preserve previous history of this repo) the template is from https://academicpages.github.io/ which is a Github Pages template for academic websites released under the MIT License. See LICENSE.md.
 
+## Installing Ruby
+You probably want to run ruby from a version manager like `chruby`, see [here](https://jekyllrb.com/docs/installation/macos/).
+
 ## Todo
   - add CMTH talks
   - fix the OG tags so that https://cards-dev.twitter.com/validator works

_drafts/sensor_watch.md

@@ -0,0 +1,22 @@
+---
+title:  Sensor Watch
+date: 2022-02-02
+layout: post
+image:
+---
+
+A while ago I backed a crowdsupply project called [Sensor Watch](https://www.oddlyspecificobjects.com/products/sensorwatch/). It's a replacement logic board for those classic Casio watches that you probably don't know the name of but have certainly seen around. This post goes through the process of getting the board swapped out and programming custom firmware on it.
+
+I also went opted for the [temperature sensor addon board](https://www.sensorwatch.net/docs/sensorboards/).
+
+## Compiling the firmware
+There is a firmware called Movement that already supports most of the things you probably want a watch to do, uses very little power and exposes a nice interface for writing extensions.
+
+
+[TOTP tokens](https://blog.singleton.io/posts/2022-10-17-otp-on-wrist/)
+
+
+
+## Future Ideas
+- [Data Runner](https://n-o-d-e.net/datarunner.html)
+- [A buzzer motor?](https://www.instructables.com/MAKE-IT-VIBRATE-Vibrator-Module-for-Casio-F-91W/)

_thesis/4_Amorphous_Kitaev_Model/4.3_AMK_Results.html

@@ -177,7 +177,7 @@ image:
 <p>Next, one could investigate whether a QSL phase may exist for other models defined on amorphous lattices with a view to more realistic prospects of observation. Do the properties of the Kitaev-Heisenberg model generalise from the honeycomb to the amorphous case? <span class="citation" data-cites="Chaloupka2010 Chaloupka2015 Jackeli2009 Kalmeyer1989 manousakis1991"> [<a href="#ref-Chaloupka2010" role="doc-biblioref">41</a>,<a href="#ref-Chaloupka2015" role="doc-biblioref">43</a>,<a href="#ref-Jackeli2009" role="doc-biblioref">72</a>–<a href="#ref-manousakis1991" role="doc-biblioref">74</a>]</span> Alternatively we might look at other lattice construction techniques. For instance we could construct lattices by linking close points <span class="citation" data-cites="agarwala2019topological"> [<a href="#ref-agarwala2019topological" role="doc-biblioref">75</a>]</span> or create simplices from random sites <span class="citation" data-cites="christRandomLatticeField1982"> [<a href="#ref-christRandomLatticeField1982" role="doc-biblioref">76</a>]</span>. Lattices constructed using these methods would likely have a large number of lattice defects where <span class="math inline">\(z \neq 3\)</span> in the bulk, leading to many localised Majorana zero modes.</p>
 <p>We found a small number of lattices for which Lieb’s theorem did not correctly predict the true ground state flux sector. I see two possibilities for what could cause this. Firstly it could be a finite size effect that is amplified by certain rare lattice configurations. It would be interesting to try to elucidate what lattice features are present when Lieb’s theorem fails. Alternatively, it might be telling that the ground state conjecture failed in the toric code A phase where the couplings are anisotropic. We showed that the colouring does not matter in the B phase. However an avenue that I did not explore was whether the particular choice of colouring for a lattice affects the physical properties in the toric code A phase. It is possible that some property of the particular colouring chosen is what leads to these rare failures of Lieb’s theorem.</p>
 <p>Overall, there has been surprisingly little research on amorphous quantum many-body phases despite there being plenty of material candidates. I expect the exact chiral amorphous spin liquid to find many generalisations to realistic amorphous quantum magnets.</p>
-<p>Next Chapter: <a href="../6_Appendices/A.1.2_Fermion_Free_Energy.html">5 Conclusion</a></p>
+<p>Next Chapter: <a href="../5_Conclusion/5_Conclusion.html">5 Conclusion</a></p>
 </section>
 </section>
 <section id="bibliography" class="level1 unnumbered">

_thesis/5_Conclusion/5_Conclusion.html

@@ -57,6 +57,10 @@ image:
  -->
 
 <!-- Main Page Body -->
+<div id="page-header">
+<p>5 Conclusion</p>
+<hr />
+</div>
 <p>This thesis has focussed on two strongly correlated systems. In these systems the many-body ground state can be complex and often cannot be reduced to or even adiabatically connected to a product state. I looked at the Falicov-Kimball (FK) model and the Kitaev Honeycomb (KH) model and defined extensions to them: the Long-Range Falicov-Kimball (LRFK) model and the Amorphous Kitaev (AK) model.</p>
 <p>These models are all exactly solvable. They contain extensively many conserved charges which allow their Hamiltonians, and crucially, the interaction terms within them, to be written in quadratic form. This allows them to be solved using the theoretical machinery of non-interacting systems. In the case of the FK and LRFK models, this solvability arises from what is essentially a separation of timescales. The heavy particles move so slowly that they can be treated as stationary. In the KH and AK models, on the other hand, the origin of the conserved degrees of freedom is more complex. Here, the algebra of the Pauli matrices interacts with the trivalent lattices on which the models are defined, to give rise to an emergent <span class="math inline">\(\mathbb{Z}_2\)</span> gauge field whose fluxes are conserved. This latter case is a beautiful example of emergence at play in condensed matter. The gauge and Majorana physics of the KH and AK models seems to arise spontaneously from nothing. Of course, this physics was hidden within the structure and local symmetries of the spin Hamiltonian all along.</p>
 <p>At first glance, exactly solvable models can seem a little too fine tuned to be particularly relevant to the real world. Surely, these models don’t spontaneously arise in nature? The models studied here provide two different ways to answer this. As we saw in <a href="../2_Background/2.1_FK_Model.html">chapter 2</a>, the FK model arises quite naturally as a limit of the Hubbard model. The Hubbard model is not exactly solvable. In fact, the FK model has been used as a way to understand more about the behaviour of the Hubbard model itself and of the Mott insulating state. We have also seen that it can provide insight into other phenomena such as disorder-free localisation. The KH model was not originally proposed as a model of any particular physical system. It was nevertheless a plausible microscopic Hamiltonian and, given its remarkable properties, it is little wonder that material candidates for Kitaev physics were quickly found. In neither case is the model expected to be a perfect description of any material. Indeed, more realistic corrections to each model are likely to break their integrability. Despite this, exactly solvable models, by virtue of being solvable, can provide important insights into the diverse physics of strongly correlated materials.</p>

_thesis/toc.html

@@ -1,13 +1,13 @@
   <ul>
   <li><a href="./1_Introduction/1_Intro.html">1 Introduction</a></li>
     <ul>
-    <li><a href="./1_Introduction/1_Intro.html">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#quantum-spin-liquids">Quantum Spin Liquids</a></li>
   </ul>
   <li><a href="./2_Background/2.1_FK_Model.html">2 Background</a></li>
     <ul>
-    <li><a href="./2_Background/2.1_FK_Model.html">The Falicov Kimball Model</a></li>
+    <li><a href="./2_Background/2.1_FK_Model.html#the-falicov-kimball-model">The Falicov 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/2.4_Disorder.html#disorder-and-localisation">Disorder and Localisation</a></li>
   </ul>
@@ -25,9 +25,10 @@
     <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>
   </ul>
+  <li><a href="./5_Conclusion/5_Conclusion.html">5 Conclusion</a></li>
   <li><a href="./6_Appendices/A.1.2_Fermion_Free_Energy.html">Appendices</a></li>
     <ul>
-    <li><a href="./6_Appendices/A.1.2_Fermion_Free_Energy.html">Evaluation of the Fermion Free Energy</a></li>
+    <li><a href="./6_Appendices/A.1.2_Fermion_Free_Energy.html#evaluation-of-the-fermion-free-energy">Evaluation of the Fermion Free Energy</a></li>
     <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.2_Markov_Chain_Monte_Carlo.html#markov-chain-monte-carlo">Markov Chain Monte Carlo</a></li>
     <li><a href="./6_Appendices/A.2_Markov_Chain_Monte_Carlo.html#a-skeleton-implementation-of-mcmc">A skeleton implementation of MCMC</a></li>

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