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Statistical Physics 7603 [Spring 2020]</span></b><br>
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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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<div><span>MoWe 9:30AM - 10:50AM</span></div>
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<div><span style="vertical-align: middle; border-width: 1px; border-style: none">Biological Sciences Bldg 676</span></div>
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<b><span style="font-family:"Times New Roman",serif; color:#201F1E; background:white">Ikes!! currently the assigned room is in a part of the campus you would not find me wandering. I will see if I can find a room closer by. </span></b></p>
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<span style="font-family: Calibri, Helvetica, sans-serif; color: rgb(134, 17, 6); background: white;">This course will introduce one of the most fundamental concepts in physics:
</span><span style="font-family: Calibri, Helvetica, sans-serif; color: rgb(134, 17, 6); background: white;"><b>the idea of universality </b></span></p>
<p style="margin: 0in 0in 0.0001pt; font-size: 12pt;"><font color="#201f1e" face="Times New Roman, serif"><span style="color: rgb(134, 17, 6); font-family: Calibri, Helvetica, sans-serif;">For experimentalists: When you take a huge amount of data, how should
you plot it? What are the relevant dimensionless variables? </span></font></p>
<p style="margin: 0in 0in 0.0001pt; font-size: 12pt;"><font color="#201f1e" face="Times New Roman, serif"><span style="color: rgb(134, 17, 6); font-family: Calibri, Helvetica, sans-serif;">For theorists: When you analyze/solve </span><span style="color: rgb(134, 17, 6); font-family: Calibri, Helvetica, sans-serif;">a<b>
</b></span><span style="color: rgb(134, 17, 6); font-family: Calibri, Helvetica, sans-serif;">model, what is its relevance for an experimental system? </span></font></p>
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<b><span style="font-family:"Times New Roman",serif; color:#201F1E; background:white"><br>
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<b style="color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sans-serif;">Prerequisites: Graduate level physics core courses</b>
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<b><span style="font-family:"Times New Roman",serif; color:#201F1E; background:white">The course should be relevant to all physicists, theorists and experimentalists.</span></b></p>
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<span style="font-family:"Times New Roman",serif; border:none windowtext 1.0pt; padding:0in">introduction to analytical and numerical methods;</span><span style=""></span></li><li style="margin:0in 0in 0.0001pt; font-size:12pt; font-family:Calibri,sans-serif; color:black; background:white">
<span style="font-family:"Times New Roman",serif; border:none windowtext 1.0pt; padding:0in">connections to experiments for each topic</span><span style=""></span></li></ul>
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<span style="font-family:"Times New Roman",serif">~ 14 weeks; 28 lectures</span></p>
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<span style="font-family:"Times New Roman",serif">Number of lectures indicated in [] brackets</span></p>
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<span style="font-family:"Times New Roman",serif">Contents:</span></p>
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<span style="font-family:"Times New Roman",serif">1. Equilibrium properties of quantum many-body systems;
</span></p>
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<span style="font-family:"Times New Roman",serif">mean field theory, high and low temperature expansions. [4]</span></p>
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<span style="font-family:"Times New Roman",serif">2. Classical phase transitions and critical phenomena;</span></p>
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<span style="font-family:"Times New Roman",serif">role of symmetries, scaling and universality;</span></p>
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<span style="font-family:"Times New Roman",serif">Ginzburg-Landau theory, gaussian fluctuations;</span></p>
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<span style="font-family:"Times New Roman",serif">Kadanoff block construction, RG transformations and relation to scaling;</span></p>
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<span style="font-family:"Times New Roman",serif"><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"> </span></p>
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<span style="font-family:"Times New Roman",serif">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">4. Information and Entropy;</span></p>
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<span style="font-family:"Times New Roman",serif">Shannon entropy, Thermodynamic vs Entanglement; Black hole entropy. [4]</span></p>
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<span style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;"><b>Evaluation:
</b>There will be no tests, or term papers. I will assign lecture follow-up/ home-work amounting to 3-5 hours per week. </span></p>
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I will expect the student to be engaged and to participate in discussions.</p>
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<u><span style="font-family:"Times New Roman",serif">References: </span></u></p>
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<span style="font-family:"Times New Roman",serif">(1) N. Goldenfeld, Lectures on Phase transitions and the Renormalization Group</span></p>
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<span style="font-family:"Times New Roman",serif">(2) An introduction to lattice gauge theory and spin systems,
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<span style="font-family:"Times New Roman",serif">J. B. Kogut, Rev. Mod. Phys. <b>51</b>, 659 (1979).</span></p>
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<span style="font-family:"Times New Roman",serif">(3) S. Sachdev, Quantum Phase Transitions</span><span style="font-family:"Times New Roman",serif"> (<span style="">Cambridge University Press), 2011.</span></span></p>
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<span style="font-family:"Times New Roman",serif">(4) </span><span style="font-family:"Times New Roman",serif">Topological phases and quantum computation, Kitaev Lecture notes at 2018 Les Houches summer school, arXiv 0904.2771</span></p>
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<u><span style="font-family:"Times New Roman",serif">Numerical Methods:</span></u></p>
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<span style="font-family:"Times New Roman",serif">Exact diagonalization, Monte Carlo, Wave function based variational methods, density matrix renormalization group [sample codes will be given]</span></p>
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