Pfeifer, Robert N. C., Buerschaper, Oliver, Trebst, Simon ORCID: 0000-0002-1479-9736, Ludwig, Andreas W. W., Troyer, Matthias ORCID: 0000-0002-1469-9444 and Vidal, Guifre (2012). Translation invariance, topology, and protection of criticality in chains of interacting anyons. Phys. Rev. B, 86 (15). COLLEGE PK: AMER PHYSICAL SOC. ISSN 1098-0121

Full text not available from this repository.

Abstract

Using finite-size scaling arguments, the critical properties of a chain of interacting anyons can be extracted from the low-energy spectrum of a finite system. Feiguin et al. [Phys. Rev. Lett. 98, 160409 (2007)] showed that an antiferromagnetic chain of Fibonacci anyons on a torus is in the same universality class as the tricritical Ising model and that criticality is protected by a topological symmetry. In the present paper we first review the graphical formalism for the study of anyons on the disk and demonstrate how this formalism may be consistently extended to the study of systems on surfaces of higher genus. We then employ this graphical formalism to study finite rings of interacting anyons on both the disk and the torus and show that analysis on the disk necessarily yields an energy spectrum which is a subset of that which is obtained on the torus. For a critical Hamiltonian, one may extract from this subset the scaling dimensions of the local scaling operators which respect the topological symmetry of the system. Related considerations are also shown to apply for open chains.

Item Type: Journal Article
Creators:
CreatorsEmailORCIDORCID Put Code
Pfeifer, Robert N. C.UNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Buerschaper, OliverUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Trebst, SimonUNSPECIFIEDorcid.org/0000-0002-1479-9736UNSPECIFIED
Ludwig, Andreas W. W.UNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Troyer, MatthiasUNSPECIFIEDorcid.org/0000-0002-1469-9444UNSPECIFIED
Vidal, GuifreUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-481107
DOI: 10.1103/PhysRevB.86.155111
Journal or Publication Title: Phys. Rev. B
Volume: 86
Number: 15
Date: 2012
Publisher: AMER PHYSICAL SOC
Place of Publication: COLLEGE PK
ISSN: 1098-0121
Language: English
Faculty: Unspecified
Divisions: Unspecified
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
QUANTUM HALL STATES; NON-ABELIAN ANYONS; FRACTIONAL STATISTICS; LANDAU-LEVEL; COMPUTATION; EXCITATIONS; DEGENERACY; ORDER; TORUSMultiple languages
Materials Science, Multidisciplinary; Physics, Applied; Physics, Condensed MatterMultiple languages
URI: http://kups.ub.uni-koeln.de/id/eprint/48110

Downloads

Downloads per month over past year

Altmetric

Export

Actions (login required)

View Item View Item