Exact Criterion for Ground-State Overlap Dominance after Quantum Quenches (opens in new tab)

Recently, conjectured and verified in TIFM model that for a sudden quench within the same physical phase region, the overlap of the initial ground state with the final eigenstates is maximal for the final ground state. We solve this problem exactly for a broad class of translationally invariant free-fermion systems. For Hamiltonians that factorize into independent $2\times2$ sectors, the final ground state is uniquely maximal if and only if th...