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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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Free Fermion Systems

Free Fermion Systems

Quantum Field Theory of Many-Body Systems

Xiao-Gang Wen

Oxford University Press

This chapter discusses quantum theory of many-fermion systems. Various correlation functions and their related physical measurements are calculated for free fermion systems at both zero and non-zero temperatures. It is pointed out that many free fermion systems resemble critical points which are on verge to change into other qualitatively different phases. The topological properties of a filled band and its relation to quantized Hall conductance are also discussed. The chapter also stresses that a many-fermion system in two and higher dimension is not really a local quantum system. In one dimension, a many-fermion system can be viewed as a local quantum system, and the Jordan–Wigner transformation is introduced to transform a 1D many-fermion system to a 1D local many-boson system. The chapter points out that the Fermi/Bose statistics are a dynamical property of the hopping Hamiltonian and come from the statistical hopping algebra.

Keywords:   Fermion, correlation functions, compressibility, spin susceptibility, diamagnetism, Jordan–Wigner transformation, statistical hopping algebra, quantized Hall conductance, topological band insulator, bosonization

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