Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach

TL;DR

This paper extends the coherent anomaly method to open quantum systems to accurately determine critical exponents in dissipative phase transitions, demonstrated on two-dimensional models with promising results from small clusters.

Contribution

It generalizes the coherent anomaly method for non-equilibrium quantum systems, enabling efficient extraction of critical exponents from cluster mean-field data.

Findings

Successfully applied to dissipative transverse-field Ising model

Achieved convergence with small clusters in 2D models

Provides a new tool for analyzing dissipative phase transitions

Abstract

We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system. The method, originally developed by Suzuki [J. Phys. Soc. Jpn. {\bf 55}, 4205 (1986)] for equilibrium systems, is based on the scaling properties of the singularity in the response functions determined through cluster mean-field calculations. We apply this method to the dissipative transverse-field Ising model and the dissipative XYZ model in two dimensions obtaining convergent results already with small clusters.