Symmetry-protected Topological Phases at Finite Temperature

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.

Contribution to the focus issue on "Artificial Graphene". Edited by Maciej Lewenstein, Vittorio Pellegrini, Marco Polini and Mordechai (Moti) Segev

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Cited by in corpus (7)

• Universalities of thermodynamic signatures in topological phases
• Ubiquity of zeros of Loschmidt amplitude for mixed states in different physical processes and their implications
• Topological characterization of one-dimensional open fermionic systems
• Conformal energy currents on the edge of a topological superconductor
• Renyi divergences, Bures geometry and quantum statistical thermodynamics
• Uhlmann phase in composite systems with entanglement
• Comparison of finite-temperature topological indicators based on Uhlmann connection