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Generalized thermalization is a process that occurs in integrable systems inwhich unitary dynamics, e.g., following a quantum quench, results in states inwhich observables after equilibration are described by generalized Gibbsensembles (GGEs). Here we discuss an emergent eigenstate construction thatallows one to built emergent local Hamiltonians of which one eigenstatecaptures the entire generalized thermalization process following a globalquantum quench. Specifically, we study the emergent eigenstate that describesthe quantum dynamics of hard-core bosons in one dimension (1D) for which theinitial state is a density wave and they evolve under a homogeneousHamiltonian.

Emergent eigenstate solution for generalized thermalization