Quantum spin ladders of non-Abelian anyons

TL;DR

This paper investigates quantum ladder systems composed of non-Abelian anyons, revealing their phase diagrams and phenomena that generalize traditional spin ladders, with implications for topological quantum fluids.

Contribution

It introduces a detailed analysis of non-Abelian anyonic ladder models, combining exact diagonalization and conformal field theory to explore their phase structure and topological features.

Findings

Identification of gapless and gapped phases in anyonic ladders

Observation of odd/even effects related to ladder width

Discovery of topological phenomena unique to 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/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.