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Extension of the adiabatic theorem

S. Damerow and S. Kehrein

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Phys. Rev. B 113, 165102 – Published 1 April, 2026

DOI: https://doi.org/10.1103/81jn-pkgb

Abstract

We examine the validity of a potential extension of the adiabatic theorem to quantum quenches, i.e., nonadiabatic changes. In particular, the transverse field Ising model (TFIM) and the axial next nearest neighbor Ising (ANNNI) model are studied. The proposed extension of the adiabatic theorem is stated as follows: Consider the overlap between the initial ground state and the postquench Hamiltonian eigenstates for quenches within the same phase. This overlap is largest for the postquench ground state. In the case of the TFIM, this conjecture is confirmed for both the paramagnetic and ferromagnetic phases numerically and analytically. In the ANNNI model, the conjecture could be analytically proven for a special case. Numerical methods are employed to investigate the conjecture's validity beyond this special case.

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synopsis

Extending the Adiabatic Theorem

Published 1 April, 2026

Like its slowly perturbed counterpart, a rapidly perturbed quantum system stays closer to the ground state than to any excited state.

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Comment on “Extension of the adiabatic theorem”

Jie Gu
Phys. Rev. B 114, 177101 (2026)

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Phys. Rev. B 113, 165102– Published 1 April, 2026
  • Received 26 May 2025
  • Revised 20 January 2026
  • Accepted 10 February 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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