Coupled spin-1/2 ladders as microscopic models for non-Abelian chiral spin liquids

TL;DR

This paper proposes a 2D lattice model of coupled spin-1/2 ladders that realizes a gapped chiral spin liquid with non-Abelian Ising topological order, supporting chiral edge modes and non-Abelian excitations.

Contribution

It introduces a novel 2D lattice construction of a non-Abelian chiral spin liquid using coupled ladders tuned to specific conformal field theories.

Findings

Numerical evidence of the c=1/2 Ising conformal field theory in the model

Demonstration of a bulk gap with chiral edge modes

Support for non-Abelian Ising anyon excitations

Abstract

We construct a two-dimensional (2D) lattice model that is argued to realize a gapped chiral spin liquid with (Ising) non-Abelian topological order. The building blocks are spin-1/2 two-leg ladders with $SU(2)$-symmetric spin-spin interactions. The two-leg ladders are then arranged on rows and coupled through SU(2)-symmetric interactions between consecutive ladders. The intra-ladder interactions are tuned so as to realize the c = 1/2 Ising conformal field theory, a fact that we establish numerically via Density Matrix Renormalization Group (DMRG) studies. Time-reversal breaking inter-ladder interactions are tuned so as to open a bulk gap in the 2D lattice system. This 2D system supports gapless chiral edge modes with Ising non-Abelian excitations but no charge excitations, in contrast to the Pfaffian non-Abelian fractional quantum Hall state.