  Generalized thermalization is a process that occurs in integrable systems in
which unitary dynamics, e.g., following a quantum quench, results in states in
which observables after equilibration are described by generalized Gibbs
ensembles (GGEs). Here we discuss an emergent eigenstate construction that
allows one to built emergent local Hamiltonians of which one eigenstate
captures the entire generalized thermalization process following a global
quantum quench. Specifically, we study the emergent eigenstate that describes
the quantum dynamics of hard-core bosons in one dimension (1D) for which the
initial state is a density wave and they evolve under a homogeneous
Hamiltonian.
