Existence of measurement-induced crossover or phase transition in the anomalous variance component V_anom

Investigate whether the anomalous contribution V_anom to the variance of the number of quantum jumps in a half-chain subsystem—defined as the term arising from the integrated many-body autocorrelation function in continuously monitored XX/XXZ spin chains—exhibits a measurement-induced crossover or a measurement-induced phase transition as the measurement strength varies, and identify concrete models or parameter regimes where such behavior occurs.

Background

The paper introduces the subsystem fluctuation of quantum jumps (SFQJ) in continuously monitored XX/XXZ spin chains and shows a measurement-induced crossover in SFQJ from Poissonian-type scaling to anomalous super-Poissonian scaling with an apparent universal exponent near 2.7 as measurement strength increases.

SFQJ is decomposed into the sum of a dynamical-activity term and an anomalous term V_anom originating from the integrated many-body autocorrelation function. While the crossover in SFQJ is driven by V_anom dominating at strong measurement, the authors’ γ-dependence analysis indicates that V_anom/L^2 itself does not display a clear crossing within the explored sizes, motivating a direct investigation into whether V_anom alone can exhibit a measurement-induced crossover or a phase transition in some models or parameter regimes.