Entanglement and localization in long-range quadratic Lindbladians

TL;DR

This paper investigates localization phenomena in open quantum systems described by long-range quadratic Lindbladians, revealing a phase transition in steady state entanglement driven by the decay exponent of bath couplings.

Contribution

It introduces a model of disordered Lindbladian dynamics with power-law bath couplings, demonstrating a stable localization transition in the steady state of an open quantum system.

Findings

Localization phase transition controlled by power-law exponent p

Steady state exhibits heterogeneity in local population imbalance

Transition remains stable with coherent hopping present

Abstract

Existence of Anderson localization is considered a manifestation of coherence of classical and quantum waves in disordered systems. Signatures of localization have been observed in condensed matter and cold atomic systems where the coupling to the environment can be significantly suppressed but not eliminated. In this work we explore the phenomena of localization in random Lindbladian dynamics describing open quantum systems. We propose a model of one-dimensional chain of non-interacting, spinless fermions coupled to a local ensemble of baths. The jump operator mediating the interaction with the bath linked to each site has a power-law tail with an exponent $p$. We show that the steady state of the system undergoes a localization entanglement phase transition by tuning $p$ which remains stable in the presence of coherent hopping. Unlike the entanglement transition in the quantum trajectories of open systems, this transition is exhibited by the averaged steady state density matrix of the Lindbladian. The steady state in the localized phase is characterised by a heterogeneity in local population imbalance, while the jump operators exhibit a constant participation ratio of the sites they affect. Our work provides a novel realisation of localization physics in open quantum systems.