Quantum Phase Transitions of Topological Insulators

TL;DR

This paper investigates quantum phase transitions in topological insulators using lattice models, revealing universal features like nodal fermions and energy non-analyticities, and explores symmetry-protected topological changes.

Contribution

It introduces a detailed analysis of topological quantum phase transitions, linking them to symmetries and topological order parameters, with a focus on universal features across different states.

Findings

Existence of nodal fermions at high symmetry points

Non-analytic third derivative of ground state energy

Jumps in topological order parameters

Abstract

In this paper, starting from a lattice model of topological insulators, we study the quantum phase transitions among different quantum states, including quantum spin Hall state, quantum anomalous Hall state and normal band insulator state by calculating their topological properties (edge states, quantized spin Hall conductivities and the number of zero mode on a Pi-flux). We find that there exist universal features for the topological quantum phase transitions (TQPTs) in different cases : the emergence of nodal fermions at high symmetry points, the non-analytic third derivative of ground state energy and the jumps of the topological "order parameters". In particular, the relation between TQPTs and symmetries of the systems are explored : different TQPTs are protected by different (global) symmetries and then described by different topological "order parameters".