Equilibrium and non-equilibrium dynamics of the sub-ohmic spin-boson model

TL;DR

This paper investigates the complex dynamics of the sub-ohmic spin-boson model using advanced numerical methods, revealing unique phase transition behaviors and oscillation phenomena relevant for quantum systems under noise.

Contribution

It provides a non-perturbative analysis of the sub-ohmic spin-boson model's dynamics, highlighting differences from the ohmic case and identifying conditions for coherent oscillations.

Findings

Delocalized phase cannot be characterized by a single energy scale.

Presence of a non-trivial quantum phase transition.

Weakly damped oscillations occur in the localized phase for s<<1.

Abstract

Employing the non-perturbative numerical renormalization group method, we study the dynamics of the spin-boson model, which describes a two-level system coupled to a bosonic bath with spectral density J(omega) propto omega^s. We show that, in contrast to the case of ohmic damping, the delocalized phase of the sub-ohmic model cannot be characterized by a single energy scale only, due to the presence of a non-trivial quantum phase transition. In the strongly sub-ohmic regime, s<<1, weakly damped coherent oscillations on short time scales are possible even in the localized phase - this is of crucial relevance, e.g., for qubits subject to electromagnetic noise.