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Topology-driven quantum phase transitions in time-reversal-invariant anyonic quantum liquids

Gils, Charlotte and Trebst, Simon and Kitaev, Alexei and Ludwig , Andreas W. W. and Troyer, Matthias and Wang, Zhenghan (2009) Topology-driven quantum phase transitions in time-reversal-invariant anyonic quantum liquids. Nature Physics, 5 (11). pp. 834-839. ISSN 1745-2473. http://resolver.caltech.edu/CaltechAUTHORS:20091208-111910640

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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.


Item Type:Article
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http://dx.doi.org/10.1038/NPHYS1396 DOIArticle
http://www.nature.com/nphys/journal/v5/n11/abs/nphys1396.htmlPublisherArticle
Additional Information:© 2009 Macmillan Publishers Limited. Received 18 September 2008; accepted 13 August 2009; published online 20 September 2009. We thank M. Freedman, X.-G. Wen and P. Fendley for stimulating discussions. Our numerical simulations were based on the ALPS libraries. A.W.W.L. was supported, in part, by NSF DMR-0706140. Author contributions: C.G., S.T. and M.T. contributed to the numerical work. C.G., A.K., A.W.W.L and Z.W. contributed to the analytical solution. All authors contributed to the development of the general picture presented in this manuscript.
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NSFDMR-0706140
Record Number:CaltechAUTHORS:20091208-111910640
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20091208-111910640
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16903
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Jan 2010 17:45
Last Modified:18 Apr 2017 21:55

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