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Ultracold Atoms in Optical LatticesSimulating quantum many-body systems$
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Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger

Print publication date: 2012

Print ISBN-13: 9780199573127

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199573127.001.0001

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Bose–Hubbard models: methods of treatment

Bose–Hubbard models: methods of treatment

(p.60) 5 Bose–Hubbard models: methods of treatment
Ultracold Atoms in Optical Lattices

Maciej Lewenstein

Anna Sanpera

Verònica Ahufinger

Oxford University Press

This chapter reviews various theoretical methods that can be applied to investigate Bose–Hubbard models. In particular, it discusses the Bogolyubov method, strong coupling expansion, the perturbative mean field approach and the Gutzwiller method, exact diagonalization, quantum Monte Carlo methods, semi-classical phase space methods, and methods specifics for 1D (Wigner-Jordan transformation, Bethe ansatz, bosonization). The chapter end with a discussion about numerical renormalization approaches in 1D (DMRG, MPS) and 2D (PEPS; MERA).

Keywords:   Bogoliubov method, strong coupling expansion, mean field methods, Gutzwiller method, exact diagonalizations, Monte Carlo methods, phase space methods, Wigner-Jordan transformation, Bethe ansatz, bosonization

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