Spins coupled to a Spin Bath: From Integrability to Chaos

Abstract

Motivated by the hyperfine interaction of electron spins with surrounding nuclei, we investigate systems of central spins coupled to a bath of noninteracting spins in the framework of random matrix theory. With increasing number of central spins a transition from Poissonian statistics to the Gaussian orthogonal ensemble occurs which can be described by a generalized Brody distribution. These observations are unaltered upon applying an external magnetic field. In the transition region, the classical counterparts of the models studied have mixed phase space.

6 pages, 5 figures included, version to appear in Phys. Rev B (Rapid Comm.)

References in corpus (8)

• Spins in few-electron quantum dots
• Driven coherent oscillations of a single electron spin in a quantum dot
• Will spin-relaxation times in molecular magnets permit quantum information processing?
• Electron Spin Dephasing due to Hyperfine Interactions with a Nuclear Spin Bath
• Electron-nuclear interaction in 13C nanotube double quantum dots
• Exact dynamics in the inhomogeneous central-spin model
• Electron spin phase relaxation of phosphorus donors in nuclear spin enriched silicon
• Exponential decay in a spin bath

Cited by in corpus (9)

• Integrable and chaotic dynamics of spins coupled to an optical cavity
• Spin polarization through Floquet resonances in a driven central spin model
• On the determinant representations of Gaudin models' scalar products and form factors
• Persistent dark states in anisotropic central spin models
• Different types of integrability and their relation to decoherence in central spin models
• Hyperfine induced spin and entanglement dynamics in Double Quantum Dots: A homogeneous coupling approach
• A variational method for integrability-breaking Richardson-Gaudin models
• Perturbative regimes in central spin models
• Unexpected systematic degeneracy in a system of two coupled Gaudin models with homogeneous couplings