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arXiv:2501.12457 · Physica A Statistical Mechanics and its Applications

Critical dynamics of the spin–boson model

Mikhail Gennag'evich Vasin, S. V. Remizov, Andrey A. Elistratov

Published Jul 22, 2026• 0 citations
arXivHTMLPDF
DOI
10.1016/j.physa.2026.131835

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The class of two-interacting-qubit spin–boson models with vanishing transverse fields on the spin-pair is studied. The model can be mapped exactly into two independent standard single-impurity spin–boson models where the role of the tunneling parameter is played by the spin–spin coupling. The dynamics of the magnetization are analyzed for different levels of (an)isotropy. The existence of a decoherence-free subspace, as well as of different classical regimes separated by a critical temperature, and symptoms of quantum (first-order and Kosterlitz–Thouless type) phase transitions in the Ohmic regime are brought to light.
The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method. We focus on the dynamical auto-correlation functions C O ( ω ) , with the operator O ^ taken as σ ^ x , σ ^ z , and X ^ , respectively. In the weak-coupling regime α < α c , these functions show power law ω -dependence in the small frequency limit, with the powers 1+2 s , 1+2 s , and s , respectively. At the critical point α = α c of the boson-unstable quantum phase transition, the critical exponents y O of these correlation functions are obtained as y σ x = y σ z = 1 − 2 s and y X = − s , respectively. Here s is the bath index and X is the boson displacement operator. Close to the spin flip point, the high frequency peak of C σ x ( ω ) is broadened significantly and the line shape changes qualitatively, showing enhanced dephasing at the spin flip point.