English

Exact Criterion for Ground-State Overlap Dominance after Quantum Quenches

Statistical Mechanics 2026-05-20 v2 Quantum Physics

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 2×22\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.

Keywords

Cite

@article{arxiv.2604.11420,
  title  = {Exact Criterion for Ground-State Overlap Dominance after Quantum Quenches},
  author = {Taisanul Haque},
  journal= {arXiv preprint arXiv:2604.11420},
  year   = {2026}
}

Comments

6 pages + 3 figures; comments are welcome