Topological Transition in a Non-Hermitian Quantum Walk

TL;DR

This paper investigates a non-Hermitian quantum walk on a bipartite lattice, revealing a topological phase transition characterized by a winding number that affects particle displacement and is robust against noise.

Contribution

It introduces a topological framework for analyzing a non-Hermitian quantum walk, linking the mean displacement to a winding number and identifying a topological phase transition.

Findings

Mean displacement is quantized and linked to the winding number.

A topological transition occurs, changing the system from pumping to non-pumping.

The transition is robust against certain noise and decoherence.

Abstract

We analyze a quantum walk on a bipartite one-dimensional lattice, in which the particle can decay whenever it visits one of the two sublattices. The corresponding non-Hermitian tight-binding problem with a complex potential for the decaying sites exhibits two different phases, distinguished by a winding number defined in terms of the Bloch eigenstates in the Brillouin zone. We find that the mean displacement of a particle initially localized on one of the non-decaying sites can be expressed in terms of the winding number, and is therefore quantized as an integer, changing from zero to one at the critical point. This problem can serve as a simplified model for nuclear spin pumping in the spin-blockaded electron transport regime of quantum dots in the presence of competing hyperfine and spin-orbital interactions. The predicted transition from pumping to non-pumping is topological in nature, and is hence robust against certain types of noise and decoherence.