Thermalization of the Lipkin-Meshkov-Glick model in blackbody radiation

n a recent work, we have derived simple Lindblad-based equations for the thermalization of systems in contactwith a thermal reservoir. Here, we apply these equations to the Lipkin-Meshkov-Glick model in contact withblackbody radiation and analyze the dipole matrix elements involved in the thermalization process. We find thatthe thermalization can be complete only if the density is sufficiently high, while, in the limit of low density, thesystem thermalizes partially, namely, within the Hilbert subspaces where the total spin has a fixed value. In thisregime, and in the isotropic case, we evaluate the characteristic thermalization time analytically, and show thatit diverges with the system size in correspondence with the critical points and inside the ferromagnetic region.Quite interestingly, at zero temperature the thermalization time diverges only quadratically with the system size,whereas quantum adiabatic algorithms, aimed at finding the ground state of the same system, imply a cubicdivergence of the required adiabatic time.