Journal
NATURE PHYSICS
Volume 5, Issue 11, Pages 834-839Publisher
NATURE PUBLISHING GROUP
DOI: 10.1038/NPHYS1396
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Funding
- NSF [DMR-0706140]
- Direct For Mathematical & Physical Scien
- Division Of Physics [0803371] Funding Source: National Science Foundation
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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 newtype 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.
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