Exact out-of-equilibrium central spin dynamics from integrability

TL;DR

This paper presents an analytical solution for the out-of-equilibrium dynamics of a central spin model with time-dependent couplings, revealing new connections to integrability and conformal field theory.

Contribution

It introduces a method to solve the Schrödinger equation exactly for specific time-dependent couplings in the Gaudin magnet, linking it to the SU(2) Wess-Zumino-Witten model.

Findings

Exact solutions for certain time-dependent couplings

New connection between integrable models and conformal field theory

Detailed analysis of a driven four-spin system

Abstract

We consider a Gaudin magnet (central spin model) with a time-dependent exchange couplings. We explicitly show that the Schr\"odinger equation is analytically solvable in terms of generalized hypergeometric functions for particular choices of the time dependence of the coupling constants. Our method establishes a new link between this system and the SU(2) Wess-Zumino-Witten model, and sheds new light on the implications of integrability in out-of-equilibrium quantum physics. As an application, a driven four-spin system is studied in detail.