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    Coherent two-state oscillations in false-vacuum decay regimes

    Peiyun Ge1,*, Xiao Wang1,2,*,†, Yu-Xin Chao1, Rong Lu1, and Li You1,2,3,4

    • *These authors contributed equally to this work.
    • †Contact author: xw970921@gmail.com

    Phys. Rev. B 113, 184306 – Published 7 May, 2026

    DOI: https://doi.org/10.1103/7qvd-yrvs

    Abstract

    Coherent two-state oscillations are observed in numerical simulations of the one-dimensional transverse-longitudinal-field Ising model within false-vacuum decay regimes. Starting from the false vacuum (a nearly fully polarized ferromagnetic state), we show that in moderate-size systems, at resonances h≈2J/n (with longitudinal field h, transverse field J, and an integer n), the expected decay can give way to coherent oscillations between the false vacuum and a symmetric resonant state. The oscillation frequency, i.e., the tunneling splitting, is notably observed to exhibit a L collective enhancement, as confirmed by a Schrieffer-Wolff analysis. In large chains, coherence remains for n≳L/2 due to bubble-size blockade and is robust against stronger transverse fields; for small n, long-range interactions can stabilize the oscillations by lifting multibubble degeneracies, establishing a robust many-body coherence mechanism beyond perturbative and finite-size limits.

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