Spectrum and Screening cloud in the central spin model

Abstract

We consider an electronic spin in a quantum dot, coupled to the surrounding nuclear spins via inhomogeneous antiferromagnetic hyperfine interactions and subject to a uniform field, which is described by Gaudin's central spin model. We study spectral properties, the two-point correlation functions, and the magnetization profile in the ground state and in low-lying excited states, which characterizes the structure of the cloud of nuclear spins screening the electron spin. A close connection to the pair occupation probability in the BCS-model is established. Using the exact Bethe Ansatz solution of that model and arguments of integrability, we can distinguish between contributions from purely classical physics and from quantum fluctuations.

26 pages, 14 figures

References in corpus (10)

• Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics
• Nuclear Spins in Nanostructures
• Exact dynamics in the inhomogeneous central-spin model
• Semiclassical dynamics and long time asymptotics of the central-spin problem in a quantum dot
• Hyperfine interaction induced decoherence of electron spins in quantum dots
• Deformed strings in the Heisenberg model
• Qubit protection in nuclear-spin quantum dot memories
• Solving the Richardson equations close to the critical points
• Quantum versus classical hyperfine-induced dynamics in a quantum dot
• Universal alternating order around impurities in antiferromagnets

Cited by in corpus (17)

• Integrability-based analysis of the hyperfine-interaction -nduced decoherence in quantum dots
• Spin decoherence due to a randomly fluctuating spin bath
• Dynamics and decoherence in the central spin model using exact methods
• Dynamics and decoherence in the central spin model in the low-field limit
• Spin-noise in the anisotropic central spin model
• Influcence of the nuclear electric quadrupolar interaction on the coherence time of hole- and electron-spins confined in semiconductor quantum dots
• Quantum model for mode locking in pulsed semiconductor quantum dots
• Competing interactions in semiconductor quantum dots
• Hyperfine induced spin and entanglement dynamics in Double Quantum Dots: A homogeneous coupling approach
• Decoherence of a single spin coupled to an interacting spin bath
• Integrability and duality in spin chains
• The Elliptic Gaudin Model: a Numerical Study
• Kinetic approach to the nuclear-spin polaron formation
• Perturbative regimes in central spin models
• Integrable model of a $p$-wave bosonic superfluid
• Exact ground state of a frustrated integer-spin modified Shastry-Sutherland model
• Finding the Dynamics of an Integrable Quantum Many-Body System via Machine Learning