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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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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 21 January 2022

Fermi and Fermi–Bose Hubbard models: methods of treatment

Fermi and Fermi–Bose Hubbard models: methods of treatment

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

Maciej Lewenstein

Anna Sanpera

Verònica Ahufinger

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199573127.003.9006

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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