Report on scipost_202301_00027v1
Year: 2023
Type: peer-review
Abstract: Central spin models provide an idealized description of interactions between a central degree of freedom and a mesoscopic environment of surrounding spins.We show that the family of models with a spin-1 at the center and XX interactions of arbitrary strength with surrounding spins is integrable.Specifically, we derive an extensive set of conserved quantities and obtain the exact eigenstates using the Bethe ansatz.As in the homogenous limit, the states divide into two exponentially large classes: bright states, in which the spin-1 is entangled with its surroundings, and dark states, in which it is not.On resonance, the bright states further break up into two classes depending on their weight on states with central spin polarization zero.These classes are probed in quench dynamics wherein they prevent the central spin from reaching thermal equilibrium.In the single spin-flip sector we explicitly construct the bright states and show that the central spin exhibits oscillatory dynamics as a consequence of the semilocalization of these eigenstates.We relate the integrability to the closely related class of integrable Richardson-Gaudin models, and conjecture that the spin-s 0 central spin XX model is integrable for any s 0 . Predictionof late-time values under the HDA 18 7.2 Comparison with the inhomogeneous model 22 8 Conclusion 23 A Counting of states in the resonant homogeneous model 24 B Expectation values at large system size under the HDA 25 C Integrability in higher spin models 27 C.1 Conserved charges far from resonance 27 C.2 Classical limit 28 C.3 Inhomogeneous Tavis-Cummings model 30 References 30
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
OpenAlex ID: W4385844236