Steady-state phases of dissipative spin-1/2 XYZ model with frustrated interaction

TL;DR

This paper explores the steady-state phases of a dissipative spin-1/2 XYZ model with frustrated interactions on a 2D lattice, revealing antiferromagnetic phases and potential limit cycle oscillations.

Contribution

It demonstrates the role of next-nearest-neighbor interactions in steady-state properties and confirms antiferromagnetic phases using cluster mean-field analysis.

Findings

Antiferromagnetic steady-state phases identified.

Evidence of limit cycle phase via quantum Lyapunov exponent.

Stability of oscillations confirmed with cluster mean-field methods.

Abstract

We investigate the steady-state phases of the dissipative spin-1/2 $J_1$-$J_2$ XYZ model on a two-dimensional square lattice. We show the next-nearest-neighboring interaction plays a crucial role in determining the steady-state properties. By means of the Gutzwiller mean-field factorization, we find the emergence of antiferromag-netic steady-state phases. The existence of such antiferromagnetic steady-state phases in thermodynamic limit is confirmed by the cluster mean-field analysis. Moreover, we find the evidence of the limit cycle phase through the largest quantum Lyapunov exponent in small cluster, and check the stability of the oscillation by calculating the averaged oscillation amplitude up to $4\times4$ cluster mean-field approximation.