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Quantum Field Theory of Many-Body SystemsFrom the Origin of Sound to an Origin of Light and Electrons$
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Xiao-Gang Wen

Print publication date: 2007

Print ISBN-13: 9780199227259

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199227259.001.0001

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Interacting Fermion Systems

Interacting Fermion Systems

Chapter:
(p.187) 5 INTERACTING FERMION SYSTEMS
Source:
Quantum Field Theory of Many-Body Systems
Author(s):

Xiao-Gang Wen

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199227259.003.05

This chapter first studies the interaction effect of a Fermi sea on a single particle propagator and the related phenomenon of orthogonality catastrophe in X-ray spectrum. It then looks at a weakly interacting Fermi gas using Hartree–Fock approximation and introduces the notion of Fermi liquid. It discusses the concept and the appearance of quasiparticle in Fermi liquid. In addition to the standard quasiparticle description of Fermi liquid, the chapter also introduces a hydrodynamic description of Fermi liquid, which can be viewed as higher dimensional bosonization. Using the spin-density-wave state as an example, it then discusses how interaction can cause instability of Fermi liquid and generate a symmetry breaking phase transition to a spin ordered phase. Several theoretical methods, such as mean-field theory, variatonal approach, and RPA method are introduced within the interacting fermion systems. The low energy O(3) non-linear sigma model for the spin ordered phase is derived, where close attention has been paid to the possible topological terms in the non-linear sigma model. The effect of topological terms on the low energy dynamics of spin waves is discussed.

Keywords:   orthogonality catastrophe, Fermi liquid theory, Hartree–Fock approximation, spin density wave, charge density wave, superconducting state, quasiparticle, topological term, spin wave, long range order

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