A model of chiral spin liquids with Abelian and non-Abelian topological phases

TL;DR

This paper introduces a 2D lattice model for quantum spin-1/2 systems that exhibits both Abelian and non-Abelian topological phases, analyzed through mean-field and RPA methods, revealing a rich phase diagram with continuous transitions.

Contribution

It presents a novel lattice model with Majorana fermions showing both Abelian and non-Abelian topological orders, expanding understanding of chiral spin liquids.

Findings

Identifies two competing chiral phases with distinct topological orders.

Demonstrates the presence of Majorana fermions propagating in the bulk.

Reveals a continuous phase transition between Abelian and non-Abelian phases.

Abstract

We present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a Random Phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, the Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.