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CompPhys, SS 14

“Computational Many Body Physics”,
Summer 2014

Meetings:

Wednesday, 4:40PM-6:10PM, Seminar room 1, MPIPKS

Lecturers:

Jens Bardarson [jensba(at)pks.mpg.de]
Frank Pollmann [frankp(at)pks.mpg.de]

Outline:

Introduction

Classical Monte Carlo simulations  (metropolis.py)

  1. Metropolis algorithm
  2. Critical slowing down: Cluster and loops algorithm
  3. Finite size scaling analysis

Exact diagonalization

  1. Construction of the Hamiltonian  (exact_diagonalization.py)
  2. Conservation of momentum (exact_diagonalization_conserve.py)
  3. Sparse matrices and the Lanczos method
  4. Evaluation of dynamical properties  (dynamical_lanczos.py)

Many body entanglement

  1. Area law
  2. Scaling in critical systems

Matrix product states

  1. AKLT
  2. Canonical form
  3. Algorithms (itebd.pyidmrg.pympo_time_evolution.py)

Tensor product states

  1. Tensor Renormalization (trg.py)
  2. Boundary theories

Quantum Monte Carlo methods

  1. Green Function Monte Carlo
  2. Stochastic Series Expansion (sse.py)

Literature

Lecture Notes by Anders W. Sandvik, http://arxiv.org/abs/1101.3281v1
Review on DMRG by Ulrich Schollwoeck, http://arxiv.org/abs/1008.3477

(Disclaimer: The codes available for download are meant for playing around with the different methods. Most examples are not super efficient and might contain serious bugs.)