Quantum dynamics of Gaudin magnets

TL;DR

This paper analytically and numerically investigates the quantum dynamics of inhomogeneous Gaudin magnets, revealing relaxation behaviors of spin correlations and Loschmidt echo, and advancing understanding of long-range quantum interactions.

Contribution

It provides explicit analytical expressions for dynamic quantities in Gaudin magnets and explores their relaxation and entanglement properties using Bethe ansatz.

Findings

Spin-spin correlations relax logarithmically to steady state.

Loschmidt echo exhibits exponential relaxation.

Insights into coherence and entanglement dynamics.

Abstract

Quantum dynamics of many-body systems is a fascinating and significant subject for both theory and experiment. The question of how an isolated many-body system evolves to its steady state after a sudden perturbation or quench still remains challenging. In this paper, using the Bethe ansatz wave function, we study the quantum dynamics of an inhomogeneous Gaudin magnet. We derive explicit analytical expressions for various local dynamic quantities with an arbitrary number of flipped bath spins, such as: the spin distribution function, the spin-spin correlation function, and the Loschmidt echo. We also numerically study the relaxation behavior of these dynamic properties, gaining considerable insight into coherence and entanglement between the central spin and the bath. In particular, we find that the spin-spin correlations relax to their steady value via a nearly logarithmic scaling, whereas the Loschmidt echo shows an exponential relaxation to its steady value. Our results advance the understanding of relaxation dynamics and quantum correlations of long-range interacting models of Gaudin type.