Braid Group and Topological Phase Transitions in Nonequilibrium Stochastic Dynamics

TL;DR

This paper demonstrates that topological phases in non-Hermitian Hamiltonians can be classified using braid group elements, revealing observable effects like oscillations and current discontinuities in nonequilibrium stochastic systems.

Contribution

It introduces a novel classification of topological phases in non-Hermitian systems using braid group theory, applied to stochastic current dynamics.

Findings

Topological phases cause decaying oscillations in probabilities.

Discontinuities are observed in steady-state current statistics.

Braid group elements effectively classify non-Hermitian topological phases.

Abstract

We show that distinct topological phases of the band structure of a non-Hermitian Hamiltonian can be classified with elements of the braid group. As the proof of principle, we consider the non-Hermitian evolution of the statistics of nonequilibrium stochastic currents. We show that topologically nontrivial phases have detectable properties, including the emergence of decaying oscillations of parity and state probabilities, and discontinuities in the steady state statistics of currents.