Non-equilibrium stationary states of quantum non-Hermitian lattice models

TL;DR

This paper demonstrates how to realize non-Hermitian lattice models in open quantum systems, revealing that steady states exhibit boundary sensitivity and particle statistics effects beyond non-Hermitian Hamiltonian predictions.

Contribution

It introduces a quantum-mechanically consistent method to realize non-Hermitian models and uncovers the complex structure of their steady states, including boundary effects and particle statistics influence.

Findings

Steady states depend on boundary conditions in a way distinct from the non-Hermitian skin effect.

Particle statistics dramatically affect the steady-state density profiles.

Steady state features cannot be fully understood from the non-Hermitian Hamiltonian alone.

Abstract

We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner by constructing an appropriate open quantum system. We focus on the quantum steady states of such models for both fermionic and bosonic systems. Surprisingly, key features and spatial structures in the steady state cannot be simply understood from the non-Hermitian Hamiltonian alone. Using the 1D Hatano-Nelson model as a paradigmatic example, we show that the steady state has a marked sensitivity to boundary conditions. This dependence however is qualitatively and quantitatively distinct from the non-Hermitian skin effect, and has no simple connection to non-Hermitian topology. Further, particle statistics play an unexpected role: the steady-state density profile is dramatically different for fermions versus bosons. Our work highlights the key role of fluctuations in quantum realizations of non-Hermitian dynamics, and provides a starting point for future work on engineered steady states of open quantum systems.