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T6: Advanced problems in quantum statistical physics – Course Topics

OUTLINE

 

1. CLASSICAL PHASE TRANSITIONS

scaling, mean field theory, Landau Theory, Renormalization group, universality classical field theories models: classical Ising models, XY chains mapping to quantum models

2. QUANTUM PHASE TRANSITIONS

quantum critical points finite temperature crossover continuum and quantum field theories models: quantum Ising model, spin chains, quantum Rotor models, Hubbard models

3. NUMERICAL SIMULATIONS

random walks Markov chains and importance sampling classical (Metropolis) Monte Carlo quantum Monte Carlo (Diffusion, Path-Integral, Determinant)

 

REFERENCE BOOKS

S. Sachdev, Quantum Phase Transitions, Cambridge University Press (1999) [Course book]

M. Le Bellac, F. Mortessagne and G. Batrouni, Equilibrium and Non-equilibrium Statistical Thermodynamics, Cambridge University Press (2004)

D.P. Landau and K. Binder, Monte Carlo Simulations in Statistical Physics, Cambridge University Press (2000)