Advanced Methods in Quantum Many-Body Theory (PH2297)
Lecturers: Lia Izabella Lovas, Ananda Roy, and Adam Smith
Lectures: Thursdays 12:00–14:00 (PH 3344)
Quantum many-body systems can exhbit extremely rich phenomena, ranging from novel phases of matter to exotic non-equilirbrium physics. Tackling such systems theretically is very challenging and requires advanced methods. This module serves as an introduction to several of these advanced analytical methods. The following topics are covered in this module:
• Bethe Ansatz techniques for zero and finite temperature thermodynamic properties of 2D classical statistical mechanical problems, 1D quantum spin chains, and 1D quantum field theories.
• The algebraic structure of topological quantum field theories (TQFTs).
• The string-net Hamiltonian construction for topologically ordered phases.
• Semiclassical methods to study out of equilibrium dynamics and transport in many-body systems, truncated Wigner approximation, quenches in the sine-Gordon model and in 1D spin chains.
"Quantum Computation and Quantum Information", Isaac Chuang and Michael Nielsen
"Exactly Solved Models in Statistical Mechanics", R. J. Baxter
"Quantum Inverse Scattering Methods and Correlation Functions", V. E. Korepin, N.M. Bogoliubov, and A.G. Izergin
“Topological Quantum: Lecture Notes (Proto-book)”, Steve Simon
“String-net condensation: A physical mechanism for topological phases”, Michael A. Levin and Xiao-Gang Wen, Phys. Rev. B 71, 045110 (2005)
"Quantum Phase Transitions", Subir Sachdev
"Phase space representations of quantum dynamics", Anatoli Polkovnikov, Annals of Phys. 325, 1790 (2010)