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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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Mean-Field Theory of Spin Liquids and Quantum Order

Mean-Field Theory of Spin Liquids and Quantum Order

Quantum Field Theory of Many-Body Systems

Xiao-Gang Wen

Oxford University Press

Topological order, as a generic phenomenon, not only appears in FQH systems, it can also appear in quantum spin systems. Quantum spin systems even allow the more general quantum order. This chapter develops a mean-field theory for the topological/quantum order in strongly interacting quantum spin systems. The mean-field theory is based on the projective construction (or the slave-particle construction). The chapter introduces the notion of projective symmetry group (PSG) to describe distinct phases that have exactly the same symmetry. PSG allows for the introduction of the notion of quantum order, which is more general then the notion of topological order. Using the mean-field theory, it calculates the phase diagram and phase transitions for quantum spin systems that do not involve change of symmetry. In fact, many phases that are studied do not break any symmetry and correspond to quantum spin liquids. The mean-field theory shows that those spin liquids can have some very exotic properties such as fractionalization, spin-charge separation, emergent gauge bosons and fermions, interacting gapless exactions, etc. The chapter finds that in addition to the symmetry breaking mechanism, PSG and quantum order is another way to produce and protect gapless excitations.

Keywords:   quantum order, projective symmetry group, PSG, spin liquid, projective construction, slave boson, slave particle, gauge theory

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