Crossovers in spin-boson and central spin models

Abstract

We discuss how the crossovers in models like spin-boson model are changed by adding the coupling of the central spin to localised modes-the latter modelled as a 'spin bath'. These modes contain most of the environmental entropy and energy at low T in solid-state systems. We find that the low T crossover between oscillator bath and spin bath dominated decoherence, occurring as one reduces the energy scale of the central spin, is characterised by very low decoherence-we show how this works out in practise in magnetic insulators. We then reconsider the standard quantum-classical crossover in the dynamics of a tunneling system, including both spin and oscillator baths. It is found that the general effect of the spin bath is to broaden the crossover in temperature between the quantum and classical activated regimes. The example of tunneling nanomagnets is used to illustrate this. The oscillator bath models assume that each bath mode is weakly perturbed, and then the description of the bath by oscillators is well known to be correct. Many physical systems are very accurately described by such models [1,3,4,6], and they are central to much of reaction rate chemistry as well. Typically one studies either a particle tunneling from a trapped state to an open continuum of states (the dissipative tunneling problem), or a doublewell system in which a particle has to go from one well to another (the dissipative 2-well problem). One has a range of temperatures in which both activation and tunneling processes are important. Both the width of the crossover regime and the detailed dependence of transition rates, as a function of temperature and applied bias, are of interest [1,5]. In the 2 well problem, the 'quantum limit', where only the 2 lowest levels of the 2-well system are relevant (assuming a weak bias between the wells), has been studied very extensively. This is the 'spin-boson model', in which a 2-level system couples to the oscillator environment.Another interesting application of the spin-boson model is to the problem of qubits in quantum information processing (QUIP). The central issue here is the study of decoherence in the dynamics of the qubit, and how it depends on both simple things like applied fields, temperature, etc., and in a more complex way on the de-

Two-level system in spin baths: Non-adiabatic dynamics and heat transport

“…Further, it is important to consider more-involved models for the reservoirs and mimic complex and realistic environments [27,28,30]: to consider baths with both harmonic and anharmonic components [56], and allow for interactions between sub-units in the bath [26,57].…”

Dynamics and thermalization of the nuclear spin bath in the single-molecule magnetMn12−ac: Test for the theory of spin tunneling

“…For comparison, we also calculate the LSR rate assuming that the electron spin tunneling is driven by spin-phonon coupling. 70,71 We anticipate that the result of this effort will be that the existing theory is not sufficient to properly describe these and other related experiments. 19,72 We shall carry out the analysis in detail in order to emphasize at every step what assumptions are being made, what is their actual validity, and why the known theories cannot explaining the data.…”

“…To this end, we shall apply the Prokof'evStamp (PS) theory of the spin bath, which describes the dynamics of a "central spin" S (here the giant electronic spin of a Mn 12 -ac cluster) coupled to a bath of environmental (in this case, nuclear) spins. In view of the complexity of the model we provide here an introductory overview of some essential elements of the PS theory needed for our analysis, referring the reader to the original papers 5,6,7,70 for more details. For comparison, we also calculate the LSR rate assuming that the electron spin tunneling is driven by spin-phonon coupling.…”

Quantum Nanomagnets and Nuclear Spins: An Overview

“…We shall come back to this issue in the review of the experimental results, but here we simply note that no phonon bath has been introduced so far, in the context of nuclear-spin mediated tunneling. A phonon-mediated tunneling rate, Γ φ , can also be calculated [19,38], yielding:…”