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Effects of interactions on the topological classification of free fermion systems

Fidkowski, Lukasz and Kitaev, Alexei (2010) Effects of interactions on the topological classification of free fermion systems. Physical Review B, 81 (13). Art. No. 134509. ISSN 1098-0121 . http://resolver.caltech.edu/CaltechAUTHORS:20100526-114410284

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Abstract

We describe in detail a counterexample to the topological classification of free fermion systems. We deal with a one-dimensional chain of Majorana fermions with an unusual T symmetry. The topological invariant for the free fermion classification lies in Z, but with the introduction of interactions the Z is broken to Z_8. We illustrate this in the microscopic model of the Majorana chain by constructing an explicit path between two distinct phases whose topological invariants are equal modulo 8, along which the system remains gapped. The path goes through a strongly interacting region. We also find the field-theory interpretation of this phenomenon. There is a second-order phase transition between the two phases in the free theory, which can be avoided by going through the strongly interacting region. We show that this transition is in the two-dimensional Ising universality class, where a first-order phase transition line, terminating at a second-order transition, can be avoided by going through the analog of a high-temperature paramagnetic phase. In fact, we construct the full phase diagram of the system as a function of the thermal operator (i.e., the mass term that tunes between the two phases in the free theory) and two quartic operators, obtaining a first-order Peierls transition region, a second-order transition region, and a region with no transition.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevB.81.134509DOIUNSPECIFIED
http://link.aps.org/doi/10.1103/PhysRevB.81.134509PublisherUNSPECIFIED
Additional Information:© 2010 The American Physical Society. Received 4 January 2010; published 7 April 2010. We would like to acknowledge useful discussions with John Preskill and Andreas Ludwig. This work was supported in part by the Institute for Quantum Information under National Science Foundation, Grant No. PHY-0803371. A.K. is also supported by DARPA under Grant No. HR0011-09- 0009.
Funders:
Funding AgencyGrant Number
Institute for Quantum Information under NSFPHY-0803371
Defense Advanced Research Projects Agency (DARPA)HR0011-09-0009
Classification Code:PACS: 71.10.Pm, 64.60.ae
Record Number:CaltechAUTHORS:20100526-114410284
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100526-114410284
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:18459
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:26 May 2010 20:54
Last Modified:26 Dec 2012 12:04

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