Ground-state phase diagram for a system of interacting, $D(D_3)$ non-Abelian anyons

TL;DR

This paper analyzes a one-dimensional model of $D(D_3)$ non-Abelian anyons, revealing a phase diagram with four regions and identifying chiral phases with non-zero ground-state momentum.

Contribution

It provides explicit ground-state energy expressions and characterizes phase transitions and chiral phases in an exactly solvable $D(D_3)$ anyon model.

Findings

Identification of four distinct ground-state phases

Explicit formulas for ground-state energies

Discovery of chiral phases with non-zero momentum

Abstract

We study an exactly solvable model of $D(D_3)$ non-Abelian anyons on a one-dimensional lattice with a free coupling parameter in the Hamiltonian. For certain values of the coupling parameter level crossings occur, which divide the ground-state phase diagram into four regions. We obtain explicit expressions for the ground-state energy in each phase, for both closed and open chain boundary conditions. For the closed chain case we show that chiral phases occur which are characterised by non-zero ground-state momentum.