Kramers' degeneracy for open systems in thermal equilibrium

TL;DR

This paper extends Kramers' degeneracy to open quantum systems at thermal equilibrium, showing that time-reversal symmetry and detailed balance protect degeneracy in the generator of dynamics, with implications for topological matter.

Contribution

It introduces a degeneracy in open fermionic systems' generators, protected by time-reversal symmetry and detailed balance, and links this to topological edge modes.

Findings

Degeneracy exists in the generator of open fermionic systems under certain symmetries.

Single-particle Green's functions reflect this degeneracy.

Microreversibility can protect topological edge signatures in open systems.

Abstract

Kramers' degeneracy theorem underpins many interesting effects in quantum systems with time-reversal symmetry. We show that the generator of dynamics for Markovian open fermionic systems can exhibit an analogous degeneracy, protected by a combination of time-reversal symmetry and the microreversibility (detailed balance) property of systems at thermal equilibrium -- the degeneracy is lifted if either condition is not met. We provide simple examples of this phenomenon and show that the degeneracy is reflected in the single-particle Green's functions. Furthermore, we show that certain experimental signatures of topological edge modes in open many-body systems can be protected by microreversibility in the same way. Our results highlight the importance of detailed balance in characterizing open topological matter.