Microscopic models of interacting Yang-Lee anyons

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 nu = 5/2. In this paper, 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 (1D) 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 1D version of the Levin-Wen model for non-unitary Yang-Lee anyons.