Ultraslow quantum dynamics in a sub-Ohmic heat bath

TL;DR

This paper investigates ultraslow quantum dynamics in a sub-Ohmic heat bath, revealing how low-frequency modes induce a dynamical asymmetry affecting spin relaxation and identifying a complex phase diagram with four distinct phases.

Contribution

It uncovers the ultraslow decay of dynamical asymmetry and characterizes a new phase with damped oscillations, expanding understanding of the sub-Ohmic spin-boson model.

Findings

Dynamical asymmetry decays ultraslowly and vanishes at equilibrium.

Identification of a novel phase with damped coherent oscillations.

Phase diagram with four distinct phases at zero temperature.

Abstract

We show that the low-frequency modes of a sub-Ohmic bosonic heat bath generate an effective dynamical asymmetry for an intrinsically symmetric quantum spin -1/2. An initially fully polarized spin first decays towards a quasiequilibrium determined by the dynamical asymmetry, thereby showing coherent damped oscillations on the (fast) time scale of the spin splitting. On top of this, the dynamical asymmetry itself decays on an ultraslow time scale and vanishes asymptotically since the global equilibrium phase is symmetric. We quantitatively study the nature of the initial fast decay to the quasiequilibrium and discuss the features of ultraslow dynamics of the quasiequilibrium itself. The dynamical asymmetry is more pronounced for smaller values of the sub-Ohmic exponent and for lower temperatures, which emphasizes the quantum many-body nature of the effect. The symmetry breaking is related to the dynamic crossover between coherent and overdamped relaxation of the spin polarization and is not connected to the localization quantum phase transition. In addition to this delocalized phase, we identify a novel phase which is characterized by damped coherent oscillations in the localized phase. This allows for a sketch of the zero-temperature phase diagram of the sub-Ohmic spin-boson model with four distinct phases.