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    Quantum criticality in sub-Ohmic systems with three competing terms: Beyond conventional spin-boson physics

    Nengji Zhou, Yulong Shen, and Zhe Sun*

    • *Contact author: sunzhe@hznu.edu.cn

    Phys. Rev. B 113, 125119 – Published 10 March, 2026

    DOI: https://doi.org/10.1103/p7vp-74cd

    Abstract

    Quantum phase transitions (QPTs) in the spin-boson model with/without the rotating-wave approximation (RWA) are systematically investigated through variational calculations using a sub-Ohmic bath with high spectral density. Four cases involving different system-environment interactions are examined, where transition points and critical exponents are accurately determined across varying tunneling strengths. Contrary to prior work, a rich phase diagram is revealed in the tunneling-coupling plane even at the low spectral exponent s<1/2, with a novel U(1)-symmetric phase being identified. As coupling increases, a multistage QPT sequence arises for the tunneling 0<Δ<Δ*=0.074(1), whereas a single transition occurs beyond this range. Furthermore, an odd-parity phase is found to emerge even under the positive tunneling, exhibiting distinct characteristics relative to the prototype model.

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