Integrability and quench dynamics in the spin-1 central spin XX model

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-$s$ central spin XX model is integrable for any $s$.

38 pages, 11 figures; (v2) minor corrections; (v3) additional level spacing data for higher spin models; (v4) minor corrections

References in corpus (16)

• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Nuclear spin physics in quantum dots: an optical investigation
• Dressed Collective Qubit States and the Tavis-Cummings Model in Circuit QED
• Dynamical Decoupling of a single electron spin at room temperature
• Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
• Exact dynamics in the inhomogeneous central-spin model
• Quantum quenches from integrability: the fermionic pairing model
• Integrability-based analysis of the hyperfine-interaction -nduced decoherence in quantum dots
• Non-adiabacity and large flucutations in a many particle Landau Zener problem
• Quantization of the Gaudin System
• Dynamics and decoherence in the central spin model using exact methods
• Shortcuts to Dynamic Polarization
• Strong-coupling emergence of dark states in XX central spin models
• Rational Lax operators and their quantization
• Blind quantum computation using the central spin Hamiltonian

Cited by in corpus (6)

• Determining the validity of cumulant expansions for central spin models
• Multifractality in the interacting disordered Tavis-Cummings model
• Integrability, multifractality, and two-photon dynamics in disordered Tavis-Cummings models
• Entanglement and energy transportation in the central-spin quantum battery
• Dark states in an integrable XY central spin model
• Exact Solvability Of Entanglement For Arbitrary Initial State in an Infinite-Range Floquet System