Exact criteria for ground-state overlap dominance and dynamical quantum phase transitions

Abstract:It was recently conjectured and verified for the transverse-field Ising model [Phys. Rev. B 113, 165102 (2026)] that, after a sudden quench within the same equilibrium phase, the initial ground state has its largest overlap with the final ground state. We show that this phase-based criterion is generally false, even in translationally invariant free-fermion systems. For Hamiltonians that factorize into independent $2\times 2$ momentum sectors, we derive the exact necessary-and-sufficient condition for ground-state overlap dominance: the initial and final sector Bloch vectors must have positive dot product for every momentum. This result proves the conjecture in classes where same-phase quenches enforce this geometric condition, but gives explicit same-phase counterexamples in Kitaev chains, where excited final eigenstates can dominate the overlap distribution. We further show that the same obstruction controls real-time Fisher-zero crossings, allowing dynamical quantum phase transitions without crossing an equilibrium phase boundary.

Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)

arXiv:2604.11420 [cond-mat.stat-mech]

(or arXiv:2604.11420v3 [cond-mat.stat-mech] for this version)

https://doi.org/10.48550/arXiv.2604.11420 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. E 114, L042103 (2026)

https://doi.org/10.1103/gxlb-k4cp Focus to learn more DOI(s) linking to related resources

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