Microscopic models of interacting Yang–Lee anyons

Abstract

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 ν = 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 modela 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.

Anyonic Chains, Topological Defects, and Conformal Field Theory

“…Therefore, it is possible that there are some non-unitary anyonic chains (see [15] for basic examples of non-unitary chains) that have D , m,…”

“…After briefly mentioning its generalizations, we move on to discuss anyonic chains [8,9,15,[17][18][19], and we review the construction of the resulting Hilbert spaces, Hamiltonians, and topological symmetries.…”

“…We will also use the fact that C in contains a set of isomorphisms, called "F-symbols", that allow us to move between different fusion channels of the objects in an associative way. The case C in = Rep [su (2) k ] was studied in [8,9,15,[17][18][19], but we will be more general.…”

“…Second, not at any point did we need to enforce unitarity (as noted in the introduction, and as will be discussed further below, some non-unitary chains may exhibit stronger topological protection of gaplessness). Indeed, non-unitary models have been considered previously [15]. The models in [15] are described by non-unitary F-symbols with non-Hermitian Hamiltonians, and the critical theories are non-unitary RCFTs.…”

“…• The Y do not map us between different Hilbert spaces 15 (examples of such situations include the topological symmetries corresponding to half-integer spins in the Rep[su(2) 4 ] spin-1 chains of [9]). …”