Dark states in an integrable XY central spin model

TL;DR

This paper demonstrates the existence of dark states in integrable XY central spin models, revealing their dependence on specific magnetic field configurations and providing explicit Bethe state constructions.

Contribution

It extends the understanding of dark states from XX models to XY models, identifying conditions for their presence and explicitly constructing the Bethe states.

Findings

Dark states exist in XY models under specific magnetic field configurations.

Explicit Bethe state constructions for these dark states are provided.

Dark states are unentangled eigenstates of the central spin in the XY model.

Abstract

Eigenstates of central spin models in which the central spin is unentangled with the environment are known as dark states. They have recently been observed in a class of integrable XX models. Here we find that dark states are present in XY models, but only for particular configurations of the central spin magnetic field. We show this via an explicit construction of the Bethe states.