Spins coupled to a Spin Bath: From Integrability to Chaos

TL;DR

This paper studies how central spins interacting with a spin bath transition from integrable to chaotic behavior, using random matrix theory, and finds a transition in spectral statistics unaffected by magnetic fields.

Contribution

It introduces a model of coupled central spins and a spin bath analyzed through random matrix theory, revealing a transition from Poissonian to GOE statistics with increasing central spins.

Findings

Transition from Poissonian to GOE spectral statistics

Generalized Brody distribution describes the transition

Magnetic field does not alter the transition behavior

Abstract

Motivated by the hyperfine interaction of electron spins with surrounding nuclei, we investigate systems of central spins coupled to a bath of noninteracting spins in the framework of random matrix theory. With increasing number of central spins a transition from Poissonian statistics to the Gaussian orthogonal ensemble occurs which can be described by a generalized Brody distribution. These observations are unaltered upon applying an external magnetic field. In the transition region, the classical counterparts of the models studied have mixed phase space.