  The goal of adiabatic ground-state preparation is to start a simple quantum
system in its ground state and adiabatically evolve the Hamiltonian to a
complex one, maintaining the ground state throughout the evolution. In
ion-trap-based quantum simulations, coherence times are too short to allow for
adiabatic evolution for large chains, so the system evolves diabatically,
creating excitations to higher energy states. Because the probability for
diabatic excitation depends exponentially on the excitation energy and because
the thermal distribution also depends exponentially on the excitation energy,
we investigate whether the diabatic excitation can create a thermal
distribution; as this could serve as an alternative for creating thermal states
of complex quantum systems without requiring contact with a heat bath. In this
work, we explore this relationship and determine situations where diabatic
excitation can approximately create such a thermal state.
