Cluster Gutzwiller Monte Carlo approach for a critical dissipative spin model

We study the influence of short-range quantum correlations and classical spatial correlations on the phase diagram of the dissipative XYZ model by using a Gutzwiller Monte carlo method and a cluster Gutzwiller ansatz for the wave function. Considering lattices of finite size we show the emergence of a ferromagnetic phase, two paramagnetic phases and the possible existence of a phase transition which is entirely quantum in nature. The inclusion of short-range quantum correlations has a drastic effect on the phase diagram but our results show the inclusion of long-range quantum correlations or the use of more sophisticated methods are needed to quantitatively match the exact results. A study of the susceptibility tensor shows that reciprocity is broken, a feature not observed in closed quantum systems.