Steady-state properties of quantum non-Hermitian lattice models

Peter Schmitteckert

A. McDonald, Ryo Hanai, Aashish A. Clerk

While the band theory of non-Hermitian Hamiltonians and the dynamics they generate have received considerable recent interest, the quantum steady states of such models remain largely unexplored. Here, the authors systematically characterize such states for fermions and bosons using an open quantum system approach. Surprisingly, these steady states exhibit features that cannot be extracted readily from the non-Hermitian Hamiltonian. This includes a macroscopic length scale which characterizes the steady-state occupation but differs from the localization length of the eigenvectors.

Marco Vekić

Pietro Brighi, Marko Ljubotina, Federico Roccati +1 more

Non-Hermitian many-body localization (NH MBL) has emerged as a possible scenario for stable localization in open systems, as suggested by spectral indicators identifying a putative transition for finite system sizes. In this work, we shift the focus to dynamical probes, specifically the steady-state spin current, to investigate transport properties in a disordered, non-Hermitian XXZ spin chain. Through exact diagonalization for small systems and tensor-network methods for larger chains, we demonstrate that the steady-state current remains finite and decays exponentially with disorder strength, showing no evidence of a transition up to disorder values far beyond the previously claimed critical point. Our results reveal a stark discrepancy between spectral indicators, which suggest localization, and transport behavior, which indicates delocalization. This highlights the importance of dynamical observables in characterizing NH MBL and suggests that traditional spectral measures may not fully capture the physics of non-Hermitian systems. Additionally, we observe a noncommutativity of limits in system size and time, further complicating the interpretation of finite-size studies. These findings challenge the existence of NH MBL in the studied model and underscore the need for alternative approaches to understanding localization in non-Hermitian settings.

Weng-Hang Leong, Ren‐Bao Liu

Ying Zhang, Lifeng Liu, Tianze Sheng +4 more

Abstract Composed of some collective excited states of an atomic ensemble, a superradiance lattice can be considered as an infinite tight‐binding model in momentum space. In this work, a non‐Hermitian superradiance lattice is realized by introducing state‐selective dissipation rates, using room‐temperature atoms. The steady‐state response of such a non‐Hermitian momentum lattice is studied with non‐Hermitian absorption spectroscopy both theoretically and experimentally. A pit‐to‐peak transition in the spectroscopy is observed when the introduced dissipation rates are tuned. Further, by accounting for the thermal motion of atoms, the Wannier Stark ladders and biorthogonal Berry phases are measured. This work hence realizes a quantum platform that can be highly useful for future experimental simulation of non‐Hermitian physics (e.g., non‐Hermitian topological lattice) with room‐temperature atoms.