System-environmental entanglement in critical spin systems under $ZZ$-decoherence and its relation to strong and weak symmetries

TL;DR

This paper studies how system-environment entanglement in critical spin chains behaves under $ZZ$-decoherence, revealing a phase transition near criticality and linking it to strong and weak symmetries through numerical analysis.

Contribution

It introduces a detailed numerical analysis of system-environment entanglement scaling and its relation to phase transitions in critical spin systems under $ZZ$-decoherence, highlighting the role of the $g$-function.

Findings

SEE exhibits a specific scaling law near criticality.

The $g$-function shows a sharp change at the phase transition.

SEE is twice as large under $ZZ$-decoherence compared to single-site $Z$-decoherence.

Abstract

Open quantum many-body systems exhibit nontrivial behavior under decoherence. In particular, system-environmental entanglement (SEE) is one of the efficient quantities for classifying mixed states subject to decoherence. In this work, we investigate the SEE of critical spin chains under nearest-neighbor $ZZ$-decoherence. We numerically show that the SEE exhibits a specific scaling law, in particular, its system-size-independent term (``$g$-function'') changes drastically its behavior in the vicinity of phase transition caused by decoherence. For the XXZ model in its gapless regime, a transition diagnosed by strong R\'{e}nyi-2 correlations occurs as the strength of the decoherence increases. We determine the location of the phase transition by investigating the $g$-function that exhibits a sharp change in the critical region of the transition. Furthermore, we find that the value of the SEE is twice that of the system under single-site $Z$-decoherence, which was recently studied by conformal field theory. From the viewpoint of R\'{e}nyi-2 Shannon entropy}, which is closely related to the SEE at the maximal decoherence, we clarify the origin of this $g$-function behavior.