Critical Dynamics of Spin Boson Model

M. G. Vasin; S. V. Remizov; A. A. Elistratov

doi:10.1016/j.physa.2026.131835

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arXiv · 2501.12457

Critical Dynamics of Spin Boson Model

M. G. Vasin·S. V. Remizov·A. A. Elistratov

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Abstract

In this work, we study the low-energy properties of the spin-boson model (SBM), which describes the dynamics of a spin-1/2 coupled to a bosonic environment characterized by a power-law spectral density $f(\omega)\propto \omega^s$. The theoretical description is based on the Schwinger--Keldysh technique combined with a Majorana spinor representation of the spin. This approach enables a renormalization group analysis of the model's critical dynamics without relying on quantum-classical mapping. We show that the transition from a delocalized to a localized state arises due to a Wilson--Fisher fixed point in both the ohmic ($s=1$) and sub-ohmic ($s<1$) cases. Our analysis recovers key results of Leggett's theory and identifies $s=1/2$ as the upper critical dimension, marking the boundary where critical exponents become mean-field. The findings are in good agreement with the predictions of quantum-classical mapping and state-of-the-art numerical data.

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M. G. Vasin, S. V. Remizov, A. A. Elistratov. 2025-01-21. Critical Dynamics of Spin Boson Model. https://doi.org/10.1016/j.physa.2026.131835

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