Integrable boundary conditions for a non-Abelian anyon chain with D(D3) symmetry

Dancer, K. A., Finch, P. E., Isaac, P. S. and Links, J. (2009) Integrable boundary conditions for a non-Abelian anyon chain with D(D3) symmetry. Nuclear Physics B, 812 3: 456-469. doi:10.1016/j.nuclphysb.2008.12.002


Author Dancer, K. A.
Finch, P. E.
Isaac, P. S.
Links, J.
Title Integrable boundary conditions for a non-Abelian anyon chain with D(D3) symmetry
Formatted title
Integrable boundary conditions for a non-Abelian anyon chain with D(D3) symmetry
Journal name Nuclear Physics B   Check publisher's open access policy
ISSN 0550-3213
1042-4687
Publication date 2009-05-11
Year available 2008
Sub-type Article (original research)
DOI 10.1016/j.nuclphysb.2008.12.002
Open Access Status DOI
Volume 812
Issue 3
Start page 456
End page 469
Total pages 14
Place of publication Amsterdam, The Netherlands
Publisher Elsevier
Language eng
Subject C1
0105 Mathematical Physics
0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
Abstract A general formulation of the Boundary Quantum Inverse Scattering Method is given which is applicable in cases where R-matrix solutions of the Yang-Baxter equation do not have the property of crossing unitarity. Suitably modified forms of the reflection equations are presented which permit the construction of a family of commuting transfer matrices. As an example, we apply the formalism to determine the most general solutions of the reflection equations for a solution of the Yang-Baxter equation with underlying symmetry given by the Drinfeld double D(D-3) Of the dihedral group D-3. This R-matrix does not have the crossing unitarity property. In this manner we derive integrable boundary conditions for an open chain model of interacting non-Abelian anyons. Crown Copyright (C) 2008 Published by Elsevier B.V. All rights reserved.
Formatted abstract
A general formulation of the Boundary Quantum Inverse Scattering Method is given which is applicable in cases where R-matrix solutions of the Yang–Baxter equation do not have the property of crossing unitarity. Suitably modified forms of the reflection equations are presented which permit the construction of a family of commuting transfer matrices. As an example, we apply the formalism to determine the most general solutions of the reflection equations for a solution of the Yang–Baxter equation with underlying symmetry given by the Drinfeld double D(D3) of the dihedral group D3. This R-matrix does not have the crossing unitarity property. In this manner we derive integrable boundary conditions for an open chain model of interacting non-Abelian anyons.
Crown Copyright © 2008 Published by Elsevier B.V. All rights reserved.
Keyword Boundary quantum inverse scattering method
Yang-Baxter equation
Drinfeld double D(D3)
Dihedral group D3
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Available online 6 December 2008

 
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Created: Mon, 15 Jun 2009, 20:54:56 EST by Cameron Harris on behalf of Faculty of Science