The spin-s homogeneous central spin model: exact spectrum and dynamics

TL;DR

This paper provides exact solutions for the spectrum and dynamics of a central spin model with arbitrary spin s interacting uniformly with a spin-1/2 bath, using algebraic and integrability methods.

Contribution

It introduces two approaches for exactly solving the spectrum of the homogeneous central spin model with arbitrary spin s, and analyzes its dynamical properties.

Findings

Exact spectrum derived using SU(2) and integrability methods

Time evolution of spin coherent states computed

Quantitative analysis of entanglement entropy, polarization, and Loschmidt echo

Abstract

We consider the problem of a central spin with arbitrary spin s that interacts pairwise and uniformly with a bath of N spins with s=1/2. We present two approaches for determining the exact spectrum of this model, one based on properties of SU(2), and the other based on integrability. We also analyze the exact time evolution of a spin coherent state, and compute the time evolution of various quantities of physical interest, including the entanglement entropy, spin polarization and Loschmidt echo.