Thermalization of long range Ising model in different dynamical regimes: a full counting statistics approach

We study thermalization of transverse field Ising chain with power law decaying interaction $\sim 1/r^{\alpha}$ following a global quantum quench of the transverse field to two different dynamical regimes. We quantify the thermalization behavior by comparing the full probability distribution function (PDF) of the evolving states with the corresponding thermal state given by the Gibbs canonical ensemble (GCE). To this end, we use matrix product state (MPS) based time dependent variational principle (TDVP) algorithm to simulate both real time evolution following a global quantum quench and the finite temperature density operator. We observe that thermalization is strongly suppressed in the region with strong confinement for all the interaction strength $\alpha$ considered whereas thermalization occurs in the region with weak confinement.