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c-theorem violation for effective central charge of infinite-randomness fixed points

Fidkowski, L. and Refael, G. and Bonesteel, N. E. and Moore, J. E. (2008) c-theorem violation for effective central charge of infinite-randomness fixed points. Physical Review B, 78 (22). Art. No. 224204. ISSN 1098-0121. https://resolver.caltech.edu/CaltechAUTHORS:FIDprb08

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Abstract

Topological insulators supporting non-Abelian anyonic excitations are in the center of attention as candidates for topological quantum computation. In this paper, we analyze the ground-state properties of disordered non-Abelian anyonic chains. The resemblance of fusion rules of non-Abelian anyons and real-space decimation strongly suggests that disordered chains of such anyons generically exhibit infinite-randomness phases. Concentrating on the disordered golden chain model with nearest-neighbor coupling, we show that Fibonacci anyons with the fusion rule tau[direct-product]tau=1[direct-sum]tau exhibit two infinite-randomness phases: a random-singlet phase when all bonds prefer the trivial fusion channel and a mixed phase which occurs whenever a finite density of bonds prefers the tau fusion channel. Real-space renormalization-group (RG) analysis shows that the random-singlet fixed point is unstable to the mixed fixed point. By analyzing the entanglement entropy of the mixed phase, we find its effective central charge and find that it increases along the RG flow from the random-singlet point, thus ruling out a c theorem for the effective central charge.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevB.78.224204DOIUNSPECIFIED
http://link.aps.org/doi/10.1103/PhysRevB.78.224204PublisherUNSPECIFIED
Additional Information:© 2008 The American Physical Society. Received 18 August 2008; published 18 December 2008. We are indebted to A. Kitaev, J. Preskill, S. Trebst, and P. Bonderson for illuminating discussions. We would like to especially thank K. Yang for his contributions to this project. G.R. and L.F. acknowledge support from NSF under Grant No. PHY-0456720. N.E.B. acknowledges support from U.S. DOE under Grant No. DE-FG02-97ER45639. J.M. acknowledges support from NSF under Grant No. DMR-0238760. We would also like to acknowledge the KITP and UCSB for their hospitality.
Funders:
Funding AgencyGrant Number
National Science FoundationPHY-0456720
Department of EnergyDE-FG02-97ER45639
National Science FoundationDMR-0238760
Subject Keywords:antiferromagnetism, anyons, entropy, ferromagnetism, Fibonacci sequences, ground states, Heisenberg model, quantum computing, quantum entanglement, renormalization
Issue or Number:22
Record Number:CaltechAUTHORS:FIDprb08
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:FIDprb08
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12687
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:19 Dec 2008 23:17
Last Modified:03 Oct 2019 00:30

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