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<b><span style="font-family:"Times New Roman",serif;mso-fareast-font-family:"Times New Roman";
color:#201F1E;background:white"></p>
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<b><span style="margin: 0px; font-family: "Times New Roman", serif; color: rgb(32, 31, 30); background: white">Advanced Statistical Physics 7603 [Spring 2020]</span></b></p>
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<b><span style="margin: 0px; font-family: "Times New Roman", serif; color: rgb(32, 31, 30); background: white">Instructor: Nandini Trivedi </span></b></p>
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<b><span style="font-family:"Times New Roman",serif;mso-fareast-font-family:"Times New Roman";
color:#201F1E;background:white"><br>
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Prerequisites: Graduate level physics core courses</span></b>
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<b><span style="font-family:"Times New Roman",serif;mso-fareast-font-family:"Times New Roman";
color:#201F1E;background:white">The course should be relevant to all physicists, theorists and experimentalists.</span></b></p>
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color:#201F1E;background:white"><br>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:"Times New Roman";
border:none windowtext 1.0pt;mso-border-alt:none windowtext 0in;
padding:0in">introduction to analytical and numerical methods;</span><span style="mso-ascii-font-family:Calibri;mso-fareast-font-family:"Times New Roman";
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri"></span></li><li style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: Calibri, sans-serif;color:black;mso-margin-top-alt:auto;mso-margin-bottom-alt:
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:"Times New Roman";
border:none windowtext 1.0pt;mso-border-alt:none windowtext 0in;
padding:0in">connections to experiments for each topic</span><span style="mso-ascii-font-family:Calibri;mso-fareast-font-family:"Times New Roman";
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri"></span></li></ul>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman"">~ 14 weeks; 28 lectures</span></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman"">Number of lectures indicated in [] brackets</span></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman""><o:p> </o:p></span></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman"">Contents:</span></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman""><o:p> </o:p></span></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman"">1. Equilibrium properties of quantum many-body systems;
</span></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman"">mean field theory, high and low temperature expansions. [4]</span></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman""><o:p> </o:p></span></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman"">2. Classical phase transitions and critical phenomena;</span></p>
<p style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: Calibri, sans-serif">
<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman"">role of symmetries, scaling and universality;</span></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman"">Ginzburg-Landau theory, gaussian fluctuations;</span></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman"">Kadanoff block construction, RG transformations and relation to scaling;</span></p>
<p style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: Calibri, sans-serif">
<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman""><span style="font-family: "Times New Roman", serif; background-color: rgb(255, 255, 255); display: inline !important">Topological defects and the </span>Berezinskii-Kosterlitz-Thouless
transition. [8]</span></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman""><o:p> </o:p></span></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman"">3. Quantum models and quantum phase transitions: Hubbard, Heisenberg, Transverse Field Ising, Toric Code, Kitaev [12]</span></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman""><o:p> </o:p></span></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman"">4. Information and Entropy;</span></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman"">Shannon entropy, Thermodynamic vs Entanglement; Black hole entropy. [4]</span></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman""><o:p> </o:p></span></p>
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<u><span style="font-family:"Times New Roman",serif;
mso-fareast-font-family:"Times New Roman"">References:
</span></u></p>
<p style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: Calibri, sans-serif">
<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman"">(1) N. Goldenfeld, Lectures on Phase transitions and the Renormalization Group</span></p>
<p style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: Calibri, sans-serif">
<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman"">(2) An introduction to lattice gauge theory and spin systems,
</span></p>
<p style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: Calibri, sans-serif">
<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman"">J. B. Kogut, Rev. Mod. Phys. <b>51</b>, 659 (1979).</span></p>
<p style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: Calibri, sans-serif">
<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman";mso-bidi-font-weight:bold">(3) S. Sachdev, Quantum Phase Transitions</span><span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman"">
(<span style="mso-bidi-font-style:italic">Cambridge University Press), 2011.</span></span></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman";mso-bidi-font-style:italic">(4)
</span><span style="font-family:"Times New Roman",serif;mso-fareast-font-family:"Times New Roman"">Topological phases and quantum computation, Kitaev Lecture notes at 2018 Les Houches summer school, arXiv 0904.2771</span></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman""><o:p> </o:p></span></p>
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<u><span style="font-family:"Times New Roman",serif;
mso-fareast-font-family:"Times New Roman"">Numerical Methods:</span></u></p>
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<span style="font-family:"Times New Roman",serif;mso-fareast-font-family:
"Times New Roman"">Exact diagonalization, Monte Carlo, Wave function based variational methods, density matrix renormalization group [sample codes will be given]</span></p>
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"Times New Roman""><o:p> </o:p></span></p>
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