Article abstract
Nature Physics 5, 834 - 839 (2009)
Published online: 20 September 2009 | doi:10.1038/nphys1396
Subject Categories: Quantum physics | Statistical physics, thermodynamics and nonlinear dynamics
Topology-driven quantum phase transitions in time-reversal-invariant anyonic quantum liquids
Charlotte Gils1, Simon Trebst2, Alexei Kitaev3, Andreas W. W. Ludwig4, Matthias Troyer1 & Zhenghan Wang2
Abstract
Indistinguishable particles in two dimensions can be characterized by anyonic quantum statistics, which is more general than that of bosons or fermions. Anyons emerge as quasiparticles in fractional quantum Hall states and in certain frustrated quantum magnets. Quantum liquids of anyons show degenerate ground states, where the degeneracy depends on the topology of the underlying surface. Here, we present a new type of continuous quantum phase transition in such anyonic quantum liquids, which is driven by quantum fluctuations of the topology. The critical state connecting two anyonic liquids on surfaces with different topologies is reminiscent of the notion of a 'quantum foam' with fluctuations on all length scales. This exotic quantum phase transition arises in a microscopic model of interacting anyons for which we present an exact solution in a linear geometry. We introduce an intuitive physical picture of this model that unifies string nets and loop gases, and provide a simple description of topological quantum phases and their phase transitions.
- Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland
- Microsoft Research, Station Q, University of California, Santa Barbara, California 93106, USA
- Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125, USA
- Department of Physics, University of California, Santa Barbara, California 93106, USA
Correspondence to: Simon Trebst2 e-mail: trebst@kitp.ucsb.edu
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