Steady-state susceptibility in continuous phase transitions of dissipative systems

TL;DR

This paper investigates the critical behaviors of fidelity and trace distance susceptibilities in dissipative systems at continuous phase transitions, analyzing two models and confirming their singular behaviors near critical points.

Contribution

It introduces a detailed analysis of susceptibility behaviors in dissipative phase transitions, validating scaling laws and critical point estimations.

Findings

Susceptibilities exhibit singular behaviors near critical points.

Critical points derived from susceptibility scaling match existing results.

Both models show consistent critical behavior patterns.

Abstract

In this work, we explore the critical behaviors of fidelity susceptibility and trace distance susceptibility associated to the steady states of dissipative systems at continuous phase transitions. We investigate on two typical models, one is the dissipative spin-1/2 XYZ model on two-dimensional square lattice and the other is a driven-dissipative Kerr oscillator. We find that the susceptibilities of fidelity and trace distance exhabit singular behaviors near the critical points of phase transitions in both models. The critical points, in thermodynamic limit, extracted from the scalings of the critical controlling parameters to the system size or nonlinearity agree well with the existed results.