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

Abstract

We investigate the dynamics of a large anisotropic spin whose easy-axis component is coupled to a bosonic bath with a spectral function . 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 (QPTs) in the sub-ohmic regime (s<1). These QPTs 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.