General topological features and instanton vacuum in quantum Hall and spin liquids

Journal Article · Fri Jul 15 04:00:00 EDT 2005 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PhysRevB.72.035329· OSTI ID:20719149

Pruisken, A M.M.; Shankar, R; Surendran, Naveen ^[1]

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1. Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)

We introduce the concept of superuniversality in quantum Hall liquids and spin liquids. This concept has emerged from previous studies of the quantum Hall effect and states that all the fundamental features of the quantum Hall effect are generically displayed as general topological features of the {theta} parameter in nonlinear {sigma} models in two dimensions. To establish superuniversality in spin liquids we revisit the mapping by Haldane who argued that the antiferromagnetic Heisenberg spin-s chain in 1+1 space-time dimensions is effectively described by the O(3) nonlinear {sigma} model with a {theta} term. By combining the path integral representation for the dimerized spin s=1/2 chain with renormalization-group decimation techniques we generalize the Haldane approach to include a more complicated theory, the fermionic rotor chain, involving four different renormalization-group parameters. We show how the renormalization-group calculation technique can be used to build a bridge between the fermionic rotor chain and the O(3) nonlinear {sigma} model with the {theta} term. As an integral and fundamental aspect of the mapping we establish the topological significance of the dangling spin at the edge of the chain. The edge spin in spin liquids is in all respects identical to the massless chiral edge excitations in quantum Hall liquids. We consider various different geometries of the spin chain such as open and closed chains, chains with an even and odd number of sides. We show that for each of the different geometries the {theta} term has a distinctly different physical meaning. We compare each case with a topologically equivalent quantum Hall liquid.

• OSTI ID: 20719149
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Journal Name: Physical Review. B, Condensed Matter and Materials Physics Journal Issue: 3 Vol. 72; ISSN 1098-0121
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANTIFERROMAGNETISM
CHIRALITY
COMPARATIVE EVALUATIONS
EXCITATION
FERMIONS
GEOMETRY
HALL EFFECT
HEISENBERG MODEL
INTEGRAL EQUATIONS
LIQUIDS
NONLINEAR PROBLEMS
PATH INTEGRALS
RENORMALIZATION
SIGMA MODEL
SPACE-TIME
SPIN
TOPOLOGY