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arXiv:2604.11420 · Physical review. E

Exact Criterion for Ground-State Overlap Dominance after Quantum Quenches

Taisanul Haque

cond-mat.stat-mechquant-phSubmitted Apr 13, 2026• Announced Apr 14, 2026• 0 citations
v1 · Apr 13, 2026v2 · May 19, 2026v3 · Oct 8, 2026
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Abstract

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 the initial and final sector Bloch vectors have positive dot product. This exact criterion proves the conjecture for large classes, but also shows that it is false in general: in Kitaev chains there are same-phase quenches for which the final ground state is not the maximal-overlap state. The same mechanism has a direct dynamical consequence, implying that same-phase quenches can generate DQPTs without crossing an physical phase boundary.

Journal reference
Phys. Rev. E 114, L042103 (2026)
DOI
10.1103/gxlb-k4cp
Comments
6 pages + 3 figures; comments are welcome

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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 2×22\times22×2 sectors, the final ground state is uniquely maximal if and only if the initial and final sector Bloch vectors have positive dot product. This exact criterion proves the conjecture for large classes, but also shows that it is false in general: in Kitaev chains there are same-phase quenches for which the final ground state is not the maximal-overlap state. The same mechanism has a direct dynamical consequence, implying that same-phase quenches can generate DQPTs without crossing an physical phase boundary.
Phys. Rev. B 113, 165102 (2026) proposed the conjecture that, for quantum quenches within the same phase, the overlap between the initial ground state and postquench eigenstates is maximal for the postquench ground state. We show that this conjecture is not valid in general. An explicit local, translationally invariant, gapped free-fermion counterexample exists even though the pre- and postquench Hamiltonians are connected by a symmetry-preserving gapped path and the thermodynamic-limit spectrum is continuous.
Dynamical phase transitions (DPTs) occur after quenching some global parameters in quantum systems, and are signalled by the nonanalytical time evolution of the dynamical free energy, which is calculated from the Loschmidt overlap between the initial and time evolved states. In a recent Letter [M. Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)], it was suggested that DPTs are closely related to equilibrium phase transitions (EPTs) for the transverse field Ising model. By studying a minimal model, the XY chain in a transverse magnetic field, we show analytically that this connection does not hold generally. We present examples where DPT occurs without crossing any equilibrium critical lines by the quench, and a nontrivial example with no DPT but crossing a critical line by the quench. Although the nonanalyticities of the dynamical free energy on the real time axis do not indicate the presence or absence of an EPT, the structure of Fisher lines for complex times reveals a qualitative difference.
We study the nonequilibrium dynamics of quenching through a quantum critical point in topological systems, focusing on one of their defining features: ground-state degeneracies and associated topological sectors. We present the notion of ``topological blocking,'' experienced by the dynamics due to a mismatch in degeneracies between two phases, and we argue that the dynamic evolution of the quench depends strongly on the topological sector being probed. We demonstrate this interplay between quench and topology in models stemming from two extensively studied systems, the transverse Ising chain and the Kitaev honeycomb model. Through nonlocal maps of each of these systems, we effectively study spinless fermionic ppp-wave paired topological superconductors. Confining the systems to ring and toroidal geometries, respectively, enables us to cleanly address degeneracies, subtle issues of fermion occupation and parity, and mismatches between topological sectors. We show that various features of the quench, which are related to Kibble-Zurek physics, are sensitive to the topological sector being probed, in particular, the overlap between the time-evolved initial ground state and an appropriate low-energy state of the final Hamiltonian. While most of our study is confined to translationally invariant systems, where momentum is a convenient quantum number, we briefly consider the effect of disorder and illustrate how this can influence the quench in a qualitatively different way depending on the topological sector considered.
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A sudden quantum quench of a Bloch band from one topological phase toward another has been shown to exhibit an intimate connection with the notion of a dynamical quantum phase transition (DQPT), where the returning probability of the quenched state to the initial state-i.e., the Loschmidt echo-vanishes at critical times {t^{*}}. Analytical results to date are limited to two-band models, leaving the exact relation between topology and DQPT unclear. In this Letter, we show that, for a general multiband system, a robust DQPT relies on the existence of nodes (i.e., zeros) in the wave function overlap between the initial band and the postquench energy eigenstates. These nodes are topologically protected if the two participating wave functions have distinctive topological indices. We demonstrate these ideas in detail for both one and two spatial dimensions using a three-band generalized Hofstadter model. We also discuss possible experimental observations.
Dynamical quantum phase transitions (DQPTs) manifested in the nonanalyticities in the temporal evolution of a closed quantum system generated by the time-independent final Hamiltonian, following a quench (or ramping) of a parameter of the Hamiltonian, is an emerging frontier of nonequilibrium quantum dynamics. We, here, introduce the notion of a dynamical topological order parameter (DTOP) that characterizes these DQPTs occurring in quenched (or ramped) two-dimensional closed quantum systems; this is quite a nontrivial generalization of the notion of DTOP introduced in Budich and Heyl [Phys. Rev. B 93, 085416 (2016)] for one-dimensional situations. This DTOP is obtained from the ``gauge-invariant'' Pancharatnam phase extracted from the Loschmidt overlap, i.e., the modulus of the overlap between the initially prepared state and its time-evolved counterpart reached following a temporal evolution generated by the time-independent final Hamiltonian. This generic proposal is illustrated considering DQPTs occurring in the subsequent temporal evolution following a sudden quench of the staggered mass of the topological Haldane model on a hexagonal lattice where it stays fixed to zero or unity and makes a discontinuous jump between these two values at critical times at which DQPTs occur. What is remarkable is that while the topology of the equilibrium model is characterized by the Chern number, the emergent topology associated with the DQPTs is characterized by a generalized winding number.