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Cited by 454

The DOI matches its Crossref record; 87 of the 87 references it cites were found in a registry or an index.

Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states andpx+ipypaired superfluids

Open access
Read, N.·2009·Physical Review B
DOI 10.1103/physrevb.79.045308
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Abstract

Many trial wave functions for fractional quantum Hall states in a single Landau level are given by functions called conformal blocks, taken from some conformal field theory. Also, wave functions for certain paired states of fermions in two dimensions, such as ${p}_{x}+i{p}_{y}$ states, reduce to such a form at long distances. Here we investigate the adiabatic transport of such many-particle trial wave functions using methods from two-dimensional field theory. One context for this is to calculate the statistics of widely separated quasiholes, which has been predicted to be non-Abelian in a variety of cases. The Berry phase or matrix (holonomy) resulting from adiabatic transport around a closed loop in parameter space is the same as the effect of analytic continuation around the same loop with the particle coordinates held fixed (monodromy), provided the trial functions are orthonormal and holomorphic in the parameters so that the Berry vector potential (or connection) vanishes. We show that this is the case (up to a simple area term) for paired states (including the Moore-Read quantum Hall state) and present general conditions for it to hold for other trial states (such as the Read-Rezayi series). We argue that trial states based on a nonunitary conformal field theory do not describe a gapped topological phase, at least in many cases. By considering adiabatic variation in the aspect ratio of the torus, we calculate the Hall viscosity, a nondissipative viscosity coefficient analogous to Hall conductivity, for paired states, Laughlin states, and more general quantum Hall states. Hall viscosity is an invariant within a topological phase and is generally proportional to the ``conformal spin density'' in the ground state.

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Metadata

Authors
Read, N.
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
2009-01-15
Volume
79
Issue
4
ISSN
  • 1098-0121 (ISSN-L)
  • 1550-235X
DOI
10.1103/physrevb.79.045308
OpenAlex
W1998185957
Cited by
454
References
87
FWCI
12.64
Type
journal article
Language
en
Open access
green

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