Higher spin Richardson-Gaudin model with time-dependent coupling: Exact dynamics

TL;DR

This paper derives the exact asymptotic wavefunction for a higher spin Richardson-Gaudin model with time-dependent coupling, revealing unique steady state properties and mean-field exactness, with experimental implications.

Contribution

It provides the first exact solution for higher spin Richardson-Gaudin models with time-dependent coupling, highlighting differences from the spin-1/2 case and mean-field validity.

Findings

Wavefunction cannot be obtained by merging spin-1/2 solutions.

Steady state is non-thermal and not a GGE.

Mean-field theory is exact for certain operator products.

Abstract

We determine the exact asymptotic many-body wavefunction of a spin-$s$ Richardson-Gaudin model with a coupling inversely proportional to time, for time evolution starting from the ground state at $t = 0^+$ and for arbitrary $s$. Contrary to common belief, the resulting wavefunction cannot be derived from the spin-$1/2$ case by merging spins, but instead requires independent treatment for each spin size. The steady state is non-thermal and, in contrast to the spin-$1/2$ case, does not conform to a natural Generalized Gibbs Ensemble. We show that mean-field theory is exact for any product of a finite number of spin operators on different sites. We discuss how these findings can be probed in cavity QED and trapped ion experiments.