The importance of level statistics for the decoherence of a central spin due to a spin environment

TL;DR

This paper investigates how the level statistics of a spin environment influence the decoherence of a central spin, revealing two regimes with distinct effects linked to frustration and level repulsion.

Contribution

It introduces a parametrized Hamiltonian to classify environments by level repulsion regimes and links these regimes to differences in decoherence efficiency.

Findings

Frustrated environments cause stronger decoherence.

Two distinct regimes of level repulsion affect decoherence differently.

Environment frustration correlates with enhanced decoherence.

Abstract

We study the decoherence of a central spin-1/2 due to a closed environment composed of spin-1/2 particles. It is known that a frustrated spin environment, such as a spin glass, is much more efficient for decoherence of the central spin than a similar size environment without frustration. We construct a Hamiltonian where the degree of frustration is parametrized by a single parameter $\kappa$. By use of this model we find that the environment can be classified by two distinct regimes with respect to the strength of level repulsion. These regimes behave qualitatively different with respect to decoherence of the central spin and might explain the strong enhancement of decoherence observed for frustrated environments.