Universal dynamics from a single-particle dark state

TL;DR

This paper reveals how a single-particle dark state in a dissipative spin chain leads to universal long-time many-body dynamics characterized by slow decay and scaling laws, confirmed by simulations.

Contribution

It uncovers the universal influence of a single-particle dark state on many-body dynamics in dissipative quantum systems, extending understanding beyond the few-excitation regime.

Findings

Zero-momentum mode decays as 1/ log t, indicating slow dissipation.

Momentum distribution exhibits universal scaling in k√t.

Total density decays as 1/√t log t, revealing long-time universal behavior.

Abstract

Open quantum systems can host dark or subradiant states whose decay is highly suppressed. While these states have been extensively studied in the few-excitation regime, their impact on the many-body dynamics remains largely unexplored. Here, we study a spin chain subject to correlated dissipation on neighboring sites, which admits a single-particle dark state at zero momentum. We show that the single-particle dark state qualitatively alters the many-body dynamics at long times, and identify its distinct universal behavior. While the zero-momentum mode is dark at the single-particle level, it decays slowly as $1/\log t$ as it becomes dressed by other modes through a dissipation-induced nonlinearity. We demonstrate that the momentum distribution takes a universal scaling form in $k\sqrt{t}$, and the total density decays as $1/\sqrt{t}\log t$. Our results further elucidate the origin of the conflicting results in recent works. Finally, we corroborate the analytics with matrix product state simulations and show that the same universal behavior persists for soft-core interactions, underscoring the universality of the emergent dynamics.