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

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