Symmetry-protected Topological Phases at Finite Temperature

TL;DR

This paper demonstrates the existence of stable symmetry-protected topological phases at finite temperature in a 2D topological insulator model, revealing thermal topological phase transitions and phase diagrams influenced by temperature and noise.

Contribution

It applies the topological Uhlmann number theory to a 2D topological insulator model, establishing the stability of SPT phases under thermal fluctuations and mapping the phase diagram.

Findings

Stable SPT phases persist at finite temperature.

Thermal topological phase transitions occur at critical temperatures.

Phase diagrams show large topological regions with thermal robustness.

Abstract

We have applied the recently developed theory of topological Uhlmann numbers to a representative model of a topological insulator in two dimensions, the Qi-Wu-Zhang model. We have found a stable symmetry-protected topological (SPT) phase under external thermal fluctuations in two-dimensions. A complete phase diagram for this model is computed as a function of temperature and coupling constants in the original Hamiltonian. It shows the appearance of large stable phases of matter with topological properties compatible with thermal fluctuations or external noise and the existence of critical lines separating abruptly trivial phases from topological phases. These novel critical temperatures represent thermal topological phase transitions. The initial part of the paper comprises a self-contained explanation of the Uhlmann geometric phase needed to understand the topological properties that it may acquire when applied to topological insulators and superconductors.