Coherent-incoherent transition in the sub-Ohmic spin-boson model

TL;DR

This paper investigates the transition from coherent to incoherent dynamics in the sub-Ohmic spin-boson model, revealing an abrupt transition influenced by coupling strength and bath spectral properties, with complex temperature effects.

Contribution

It introduces a variational approach to analyze the transition in the sub-Ohmic spin-boson model, highlighting non-monotonic temperature dependence and re-entrance phenomena near the transition point.

Findings

Transition is abrupt and exists for all 0<s<1

Non-monotonic temperature dependence of the two-level gap

Re-entrance regime near the transition due to low-frequency bath modes

Abstract

We study the spin-boson model with a sub-Ohmic bath using a variational method. The transition from coherent dynamics to incoherent tunneling is found to be abrupt as a function of the coupling strength $\alpha$ and to exist for any power $0 < s< 1$, where the bath coupling is described by $J(\omega) \sim \alpha \omega^{s}$. We find non-monotonic temperature dependence of the two-level gap $\tilde{K}$ and a re-entrance regime close to the transition due to non-adiabatic low-frequency bath modes. Differences between thermodynamic and dynamic conditions for the transition as well as the limitations of the simplified bath description are discussed.