Dynamical properties of dissipative XYZ Heisenberg lattices

TL;DR

This paper investigates the dynamical behavior of dissipative XYZ Heisenberg lattices, revealing that critical dissipative magnetic phase transitions occur in 2D but not in 1D, with insights from quantum trajectories.

Contribution

It provides the first detailed analysis of the critical dynamics in dissipative XYZ Heisenberg lattices across different dimensions, combining mean-field, numerical, and trajectory methods.

Findings

Critical dynamics in 2D lattices near phase transition

No critical dynamics observed in 1D lattices

Quantum trajectories reveal transition nature

Abstract

We study dynamical properties of dissipative XYZ Heisenberg lattices where anisotropic spin-spin coupling competes with local incoherent spin flip processes. In particular, we explore a region of the parameter space where dissipative magnetic phase transitions for the steady state have been recently predicted by mean-field theories and exact numerical methods. We investigate the asymptotic decay rate towards the steady state both in 1D (up to the thermodynamical limit) and in finite-size 2D lattices, showing that critical dynamics does not occur in 1D, but it can emerge in 2D. We also analyze the behavior of individual homodyne quantum trajectories, which well reveal the nature of the transition.