Universität zu Köln

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

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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:	Creators Email ORCID ORCID Put Code Pfeifer, Robert N. C. UNSPECIFIED UNSPECIFIED UNSPECIFIED Buerschaper, Oliver UNSPECIFIED UNSPECIFIED UNSPECIFIED Trebst, Simon UNSPECIFIED orcid.org/0000-0002-1479-9736 UNSPECIFIED Ludwig, Andreas W. W. UNSPECIFIED UNSPECIFIED UNSPECIFIED Troyer, Matthias UNSPECIFIED orcid.org/0000-0002-1469-9444 UNSPECIFIED Vidal, Guifre UNSPECIFIED UNSPECIFIED UNSPECIFIED
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:	Keywords Language QUANTUM HALL STATES; NON-ABELIAN ANYONS; FRACTIONAL STATISTICS; LANDAU-LEVEL; COMPUTATION; EXCITATIONS; DEGENERACY; ORDER; TORUS Multiple languages Materials Science, Multidisciplinary; Physics, Applied; Physics, Condensed Matter Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/48110