Microscopic models of interacting Yang-Lee anyons

Details Microscopic models of interacting Yang-Lee anyons Microscopic models of interacting Yang-Lee anyons

2010-12-06

arxiv.org/abs/1012.1080v1

New J. Phys. 13, 045006 (2011)

Physics

Condensed Matter

Strongly Correlated Electrons

16 pages, 15 figures

Scientific paper

10.1088/1367-2630/13/4/045006

Collective states of interacting non-Abelian anyons have recently been studied mostly in the context of certain fractional quantum Hall states, such as the Moore-Read state proposed to describe the physics of the quantum Hall plateau at filling fraction v = 5/2. In this manuscript, we further expand this line of research and present non-unitary generalizations of interacting anyon models. In particular, we introduce the notion of Yang-Lee anyons, discuss their relation to the so-called `Gaffnian' quantum Hall wave function, and describe an elementary model for their interactions. A one-dimensional version of this model -- a non-unitary generalization of the original golden chain model -- can be fully understood in terms of an exact algebraic solution and numerical diagonalization. We discuss the gapless theories of these chain models for general su(2)_k anyonic theories and their Galois conjugates. We further introduce and solve a one-dimensional version of the Levin-Wen model for non-unitary Yang-Lee anyons.

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