Quantum jump correlations in long-range dissipative spin systems via cluster and cumulant expansions

TL;DR

This paper investigates how quantum jump trajectories reveal phase transitions and correlations in long-range dissipative spin systems, using cluster and cumulant expansion methods.

Contribution

It introduces a combined approach of cluster mean-field and cumulant expansions to analyze quantum jump correlations and phase transitions in open quantum systems.

Findings

Quantum jump correlations signal different phases clearly.

Distinct dynamical features are observed across the phase transition.

Trajectory-resolved observables serve as effective probes of collective behavior.

Abstract

We characterize nonequilibrium phases in long-range dissipative spin systems through the statistical properties of quantum jump trajectories. While the average dynamics governed by the Lindblad master equation provides access to steady-state expectation values of order parameters, the quantum trajectory framework reveals features encoded in the spatial and temporal correlations of detection events. Focusing on a model exhibiting a paramagnetic-to-ferromagnetic phase transition, we investigate the full counting statistics of quantum jumps using a tilted Lindbladian approach. We combine this with cluster mean-field and cumulant expansion techniques, which allow us to capture, respectively, the short- and long-range structure of jump correlations. In addition, we study the waiting-time distributions of detection events. We show that quantum jump correlations display clear signatures of the underlying phases and reveal distinct dynamical features across the transition. Our results highlight the potential of trajectory-resolved observables as probes of collective behavior in open quantum many-body systems and provide new insights into the role of long-range interactions in shaping nonequilibrium dynamics.