Course Announcement: Advanced Statistical Mechanics 7603 Spring 2020

[Trivedi, Nandini]

Advanced Statistical Physics 7603 [Spring 2020]

Instructor: Nandini Trivedi

MoWe 9:30AM - 10:50AM
Biological Sciences Bldg 676


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.


This course will introduce one of the most fundamental concepts in physics: the idea of universality

For experimentalists: When you take a huge amount of data, how should you plot it? What are the relevant dimensionless variables?

For theorists: When you analyze/solve a model, what is its relevance for an experimental system?


Prerequisites: Graduate level physics core courses

The course should be relevant to all physicists, theorists and experimentalists.


  *   introduction to analytical and numerical methods;
  *   connections to experiments for each topic


~ 14 weeks; 28 lectures

Number of lectures indicated in [] brackets



Contents:



1. Equilibrium properties of quantum many-body systems;

mean field theory, high and low temperature expansions. [4]



2. Classical phase transitions and critical phenomena;

role of symmetries, scaling and universality;

Ginzburg-Landau theory, gaussian fluctuations;

Kadanoff block construction, RG transformations and relation to scaling;

Topological defects and the Berezinskii-Kosterlitz-Thouless transition.  [8]



3. Quantum models and quantum phase transitions: Hubbard, Heisenberg, Transverse Field Ising, Toric Code, Kitaev [12]



4. Information and Entropy;

Shannon entropy, Thermodynamic vs Entanglement; Black hole entropy. [4]



Evaluation: There will be no tests, or term papers. I will assign lecture follow-up/ home-work amounting to 3-5 hours per week.

I will expect the student to be engaged and to participate in discussions.


References:

(1) N. Goldenfeld, Lectures on Phase transitions and the Renormalization Group

(2) An introduction to lattice gauge theory and spin systems,

J. B. Kogut, Rev. Mod. Phys. 51, 659 (1979).

(3) S. Sachdev, Quantum Phase Transitions (Cambridge University Press), 2011.

(4) Topological phases and quantum computation, Kitaev Lecture notes at 2018 Les Houches summer school, arXiv 0904.2771



Numerical Methods:

Exact diagonalization, Monte Carlo, Wave function based variational methods, density matrix renormalization group [sample codes will be given]



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