Exact Criterion for Ground-State Overlap Dominance after Quantum Quenches

TL;DR

This paper challenges a recent conjecture by deriving an exact condition for ground-state overlap dominance after quantum quenches in free-fermion systems, revealing exceptions and implications for dynamical phase transitions.

Contribution

It provides the first exact necessary-and-sufficient criterion for ground-state overlap dominance in free-fermion systems and identifies counterexamples to the previous conjecture.

Findings

The phase-based criterion is generally false in free-fermion systems.

Derived the exact condition: initial and final Bloch vectors must have positive dot product for all momenta.

Identified counterexamples in Kitaev chains where excited states dominate overlaps.

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.