Dynamics of open quantum spin systems: An assessment of the quantum master equation approach

TL;DR

This paper evaluates the effectiveness of the quantum master equation approach, specifically the Bloch equation with time-independent coefficients, in accurately modeling the dynamics of a spin-1/2 particle interacting with a thermal bath, using numerical solutions as benchmarks.

Contribution

It demonstrates that a Bloch-type quantum master equation with constant coefficients can reliably describe spin dynamics, and compares its coefficients with those from the Redfield equation.

Findings

The Bloch equation provides accurate dynamics for most cases.

Redfield equation coefficients differ significantly from numerical estimates.

Numerical solutions validate the Markovian quantum master equation approach.

Abstract

Data of the numerical solution of the time-dependent Schr\"odinger equation of a system containing one spin-1/2 particle interacting with a bath of up to 32 spin-1/2 particles is used to construct a Markovian quantum master equation describing the dynamics of the system spin. The procedure of obtaining this quantum master equation, which takes the form of a Bloch equation with time-independent coefficients, accounts for all non-Markovian effects in as much the general structure of the quantum master equation allows. Our simulation results show that, with a few rather exotic exceptions, the Bloch-type equation with time-independent coefficients provides a simple and accurate description of the dynamics of a spin-1/2 particle in contact with a thermal bath. A calculation of the coefficients that appear in the Redfield master equation in the Markovian limit shows that this perturbatively derived equation quantitatively differs from the numerically estimated Markovian master equation, the results of which agree very well with the solution of the time-dependent Schr\"odinger equation.