Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p(x) + ip(y) paired superfluids
By N. Read. 2008
340 citations recorded by the source corpus.
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.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/1e91f4c5755fab4ede3ad08153c96ef6a16dce23
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In Atomic and Molecular Physics, and Optics
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Citations in the corpus
- Parity-violating hydrodynamics in 2 + 1 dimensions (2011, methodology): “In 2+1 dimensions the parity-odd analogue of the shear viscosity, which is called the Hall viscosity, has been studied from the condensed matter physics perspective in [6, 16–19], using an effective field theory [7,20], and also using the AdS/CFT correspondence [10, 21–23].”
- Adiabatic hydrodynamics: the eightfold way to dissipation (2015, background): “While we have not quite justified why {N [(μν)|(αβ)],S [μν]} should be thought of as configuration space curvatures, supporting evidence for this interpretation can be advanced by examining the physics of Hall viscosity [58].”
- Quantum Hall physics : Hierarchies and conformal field theory techniques (2016, methodology): “For the CFT hierarchy construction, we shall need the modular transformations of the multicomponent wave functions, which can be derived using the techniques employed by Read (2009b) for the Laughlin case.”
- Geometry and Response of Lindbladians (2015, neutral): “For a closed path (xð1Þ α 1⁄4 xð0Þ α ) and assuming Aα;00 is defined uniquely for the whole path [146], the state transforms as jψð0Þi → Bjψð0Þi, with resulting gauge-invariant holonomy (here, Berry phase)”
- Torsional anomalies, Hall viscosity, and bulk-boundary correspondence in topological states (2012, background): “QHE with rotation[8, 9] and translation invariance[10], and chiral superconductors[8, 11].”