Quantum criticality of the sub-ohmic spin-boson model

Abstract

We revisit the critical behavior of the sub-ohmic spin-boson model. Analysis of both the leading and subleading terms in the temperature dependence of the inverse static local spin susceptibility at the quantum critical point, calculated using a numerical renormalization-group method, provides evidence that the quantum critical point is interacting in cases where the quantum-to-classical mapping would predict mean-field behavior. The subleading term is shown to be consistent with an w/T scaling of the local dynamical susceptibility, as is the leading term. The frequency and temperature dependences of the local spin susceptibility in the strong-coupling (delocalized) regime are also presented. We attribute the violation of the quantum-to-classical mapping to a Berry-phase term in a continuum path-integral representation of the model. This effect connects the behavior discussed here with its counterparts in models with continuous spin symmetry.

9 pages, 10 figures

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• Nonequilibrium Dynamics Across an Impurity Quantum Critical Point
• Quantum phase transitions in the spin-boson model without the counterrotating terms
• Improved Silbey-Harris polaron ansatz for the spin-boson model
• Green's functions for spin boson systems: Beyond conventional perturbation theories
• Quantum tricritical point emerging in the spin-boson model with two dissipative spins in staggered biases
• Consistent perturbative treatment of the subohmic spin-boson model yielding arbitrarily small $T_2/T_1$ decoherence time ratios
• Single Mode Approximation for sub-Ohmic Spin-Boson Model: Adiabatic Limit and Critical Properties