Dynamics and decoherence in the central spin model in the low-field limit

TL;DR

This paper combines analytic and numerical methods, including density matrix renormalization group techniques, to study the dynamics and decoherence of a central spin interacting with a large spin bath in the low-field limit.

Contribution

It introduces a novel application of density matrix renormalization group to the central spin model and assesses semiclassical approximations for this quantum system.

Findings

DMRG effectively captures hyperfine interactions in large spin baths.

Semiclassical models partially reproduce quantum dynamics.

The study provides insights into decoherence mechanisms at low magnetic fields.

Abstract

We present a combination of analytic calculations and a powerful numerical method for large spin baths in the low-field limit. The hyperfine interaction between the central spin and the bath is fully captured by the density matrix renormalization group. The adoption of the density matrix renormalization group for the central spin model is presented and a proper method for calculating the real-time evolution at infinite temperature is identified. In addition, we study to which extent a semiclassical model, where a quantum spin-1/2 interacts with a bath of classical Gaussian fluctuations, can capture the physics of the central spin model. The model is treated by average Hamiltonian theory and by numerical simulation.