Topological characterization of quantum phase transitions in a S=1/2 spin model

TL;DR

This paper introduces a new Majorana spin representation and demonstrates that a Kitaev model on a brick-wall lattice exhibits topological quantum phase transitions characterized by nonlocal string order parameters, which can be transformed into local order parameters.

Contribution

It presents a novel Majorana representation of S=1/2 spins and shows that a Kitaev model on a brick-wall lattice is equivalent to non-interacting Majorana fermions with Z_2 gauge fields, enabling topological phase transition analysis.

Findings

Quantum phase transitions are topological in nature.

String order parameters characterize the phase transitions.

Dual representations convert nonlocal order parameters into local ones.

Abstract

We have introduced a novel Majorana representation of S=1/2 spins using the Jordan-Wigner transformation and have shown that a generalized spin model of Kitaev defined on a brick-wall lattice is equivalent to a model of non-interacting Majorana fermions with Z_2 gauge fields without redundant degrees of freedom. The quantum phase transitions of the system at zero temperature are found to be of topological type and can be characterized by nonlocal string order parameters. In appropriate dual representations, these string order parameters become local order parameters and the basic concept of Landau theory of continuous phase transition can be applied.