From quantum-mechanical to classical dynamics in the central-spin model

TL;DR

This paper explores the transition from quantum to classical dynamics in the central-spin model, demonstrating that classical approximations can accurately reproduce quantum results for large baths and moderate magnetic fields, thus enabling efficient simulations.

Contribution

It extends previous semiclassical approaches by explicitly conserving total spin and compares classical and quantum dynamics, showing their agreement under certain conditions.

Findings

Classical dynamics match quantum results for large bath sizes.

Conservation of total spin improves semiclassical approximations.

Classical equations of motion are effective for specific parameter regimes.

Abstract

We discuss the semiclassical and classical character of the dynamics of a single spin 1/2 coupled to a bath of noninteracting spins 1/2. On the semiclassical level, we extend our previous approach presented in D. Stanek, C. Raas, and G. S. Uhrig, Phys. Rev. B 88, 155305 (2013) by the explicit consideration of the conservation of the total spin. On the classical level, we compare the results of the classical equations of motions in absence and presence of an external field to the full quantum result obtained by density-matrix renormalization (DMRG). We show that for large bath sizes and not too low magnetic field the classical dynamics, averaged over Gaussian distributed initial spin vectors, agrees quantitatively with the quantum-mechanical one. This observation paves the way for an efficient approach for certain parameter regimes.