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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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Fermi and Fermi–Bose Hubbard models: methods of treatment

Fermi and Fermi–Bose Hubbard models: methods of treatment

(p.98) 6 Fermi and Fermi–Bose Hubbard models: methods of treatment
Ultracold Atoms in Optical Lattices

Maciej Lewenstein

Anna Sanpera

Verònica Ahufinger

Oxford University Press

This chapter presents various methods specific for fermionic systems and Fermi–Bose mixtures. It starts by discussing a lattice version of the BCS theory and then reviews BCS-BEC crossover theory for trapped Fermi gases close to the Feshbach resonance. The chapter analyses Fermi Hubbard models in the strongly correlated regime and t-J limit, and introduces the Gutzwiller projection method and the slave boson approach. It discusses in detail, in particular in the context of Fermi-Bose mixtures, effective low energy Hamiltonians and their derivation.

Keywords:   Fermi Hubbard model, BCS theory, BCS-BEC crossover, Feshbach resonance, Gutzwiller projection method, slave boson theory, t-J model, effective Hamiltonian

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