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  • Letter
  • Open Access

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

Taisanul Haque*

  • *Contact author: taisanul.haque@stud.uni-goettingen.de
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Phys. Rev. E 114, L042103 – Published 8 October, 2026

DOI: https://doi.org/10.1103/gxlb-k4cp

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 2×2 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.

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Information

Phys. Rev. E 114, L042103– Published 8 October, 2026
  • Received 15 April 2026
  • Accepted 25 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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