Microscopic models of interacting Yang-Lee anyons

TL;DR

This paper introduces non-unitary Yang-Lee anyons, explores their relation to quantum Hall states, and provides exact solutions for one-dimensional models, expanding the understanding of interacting non-Abelian anyons.

Contribution

It presents the first non-unitary generalizations of interacting anyon models, including algebraic solutions and numerical analysis of 1D chains and Levin-Wen models.

Findings

Exact solutions for 1D Yang-Lee anyon chains

Connection to Gaffnian quantum Hall wave function

Analysis of gapless theories for su(2)_k anyons

Abstract

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.