Dynamics of large anisotropic spin in a sub-ohmic dissipative environment close to a quantum-phase transition

TL;DR

This paper studies the quantum dynamics of a large anisotropic spin coupled to a sub-ohmic bosonic bath, revealing quantum-phase transitions only for integer spins and analyzing decoherence and oscillations near these transitions.

Contribution

It provides a non-perturbative renormalization group analysis of quantum-phase transitions in large anisotropic spins with sub-ohmic environments, highlighting differences between integer and half-integer spins.

Findings

Quantum-phase transitions occur only for integer spins in the sub-ohmic regime.

Half-integer spins exhibit fixed points similar to the spin-boson model without tunneling.

Short-time coherent oscillations persist even in the localized phase.

Abstract

We investigate the dynamics of a large anisotropic spin whose easy-axis component is coupled to a bosonic bath with a spectral function $J(\w)\propto \omega^s$. Such a spin complex might be realized in a single-molecular magnet. Using the non-perturbative renormalization group, we calculate the line of quantum-phase transitions in the sub-ohmic regime ($s<1$). These quantum-phase transitions only occur for integer spin $J$. For half-integer $J$, the low temperature fixed-point is identical to the fixed-point of the spin-boson model without quantum-tunneling between the two levels. Short-time coherent oscillations in the spin decay prevail even into the localized phase in the sub-ohmic regime. The influence of the reorganization energy and the recurrence time on the decoherence in the absence of quantum-tunneling is discussed.