Abstract
We investigate the steady-state phases of the dissipative spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ 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 (MF) factorization, we find the emergence of antiferromagnetic (AFM) steady-state phases. The existence of such AFM steady-state phases in thermodynamic limit is confirmed by cluster mean-field (CMF) analysis. Moreover, we find 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 $4\ifmmode\times\else\texttimes\fi{}4$ CMF approximation.
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