Mean-field validity in a dissipative critical system: Liouvillian gap, $\mathbb{PT}$-symmetric antigap, and permutational symmetry in the $XYZ$ model

Understand

We study the all-to-all connected $XYZ$ (anisotropic-Heisenberg) spin model with local and collective dissipations, comparing the results of mean field theory with the solution of the Lindblad quantum evolution.

• Leveraging the permutational symmetry of the model [N.
• Shammah et al., Phys Rev.
• A 98, 063815 (2018)], we find exactly (up to numerical precision) the steady state up to $N=95$ spins.