Quantum spin ladders of non-Abelian anyons

Abstract

Quantum ladder models, consisting of coupled chains, form intriguing systems bridging one and two dimensions and have been well studied in the context of quantum magnets and fermionic systems. Here we consider ladder systems made of more exotic quantum mechanical degrees of freedom, so-called non-Abelian anyons, which can be thought of as certain quantum deformations of ordinary SU(2) spins. Such non-Abelian anyons occur as quasiparticle excitations in topological quantum fluids, including ${p}_{x}+i{p}_{y}$ superconductors, certain fractional quantum Hall states, and rotating Bose-Einstein condensates. Here we use a combination of exact diagonalization and conformal field theory to determine the phase diagrams of ladders with up to four chains. We discuss how phenomena familiar from ordinary SU(2) spin ladders are generalized in their anyonic counterparts, such as gapless and gapped phases, odd and even effects with the ladder width, and elementary ``magnon'' excitations. Other features are entirely due to the topological nature of the anyonic degrees of freedom. In general, two-dimensional systems of interacting localized non-Abelian anyons are anyonic generalizations of two-dimensional quantum magnets.