Universal scaling at a pre-thermal dark state

TL;DR

This paper investigates universal dynamical scaling in a non-Hermitian quantum model, revealing a prethermal dark state where coherent dynamics persist despite dissipation, with unique short-time scaling behavior.

Contribution

It demonstrates that short-time universal scaling can occur in non-Hermitian systems due to a prethermal dark state, contrasting with the typical loss of universality.

Findings

Universal scaling is restored at short times in a non-Hermitian $O(N)$ model.

A distinct initial slip exponent indicates different short-time dynamics from closed systems.

Dissipation effects are compensated by interactions, enabling observable coherent many-body dynamics.

Abstract

Recent experimental and theoretical progress as well as the prospect of commercially viable quantum technologies have inspired great interest in the study of open quantum systems and their dynamics. Many open quantum systems are well described by an effective non-Hermitian Hamiltonian generating a time evolution that allows eigenstates to decay and dissipate to the environment. In this framework, quantum coherent scaling is traditionally tied to the appearance of dark states, where the effect of dissipation becomes negligible. Here, we discuss the universal dynamical scaling after a sudden quench of the non-Hermitian $O(N)$ model Hamiltonian. While universality is generally spoiled by non-Hermiticity, we find that for a given set of internal parameters short-time scaling behaviour is restored with an initial slip exponent profoundly different from that of closed quantum systems. This result is tied to the compensation of dissipation by interaction effects at short times leading to a prethermal dark state, where coherent many-body dynamics can be still observed.