Efficient algorithms for the dynamics of large and infinite classical central spin models

Abstract

We investigate the time dependence of correlation functions in the central spin model, which describes the electron or hole spin confined in a quantum dot, interacting with a bath of nuclear spins forming the Overhauser field. For large baths, a classical description of the model yields quantitatively correct results. We develop and apply various algorithms in order to capture the long-time limit of the central spin for bath sizes from 1000 to infinitely many bath spins. Representing the Overhauser field in terms of orthogonal polynomials, we show that a carefully reduced set of differential equations is sufficient to compute the spin correlations of the full problem up to very long times, for instance up to $10^5\hslash /J_{\mathrm{Q}}$ where $J_{\mathrm{Q}}$ is the natural energy unit of the system. This technical progress renders an analysis of the model with experimentally relevant parameters possible. We benchmark the results of the algorithms with exact data for a small number of bath spins and we predict how the long-time correlations behave for different effective numbers of bath spins.

13 pages, 12 figures

References in corpus (17)

• Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics
• Nuclear spin physics in quantum dots: an optical investigation
• Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
• Quantum many-body theory of qubit decoherence in a finite-size spin bath
• Electron spin decoherence of single Nitrogen-Vacancy defects in diamond
• Exact dynamics in the inhomogeneous central-spin model
• Quantum many-body theory of qubit decoherence in a finite-size spin bath. II. Ensemble dynamics
• Integrability-based analysis of the hyperfine-interaction -nduced decoherence in quantum dots
• Quantum Decoherence of the Central Spin in a Sparse System of Dipolar Coupled Spins
• Nonperturbative master equation solution of central spin dephasing dynamics
• 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
• Non-Markovian dynamics of a single electron spin coupled to a nuclear spin bath
• Dynamics and decoherence in the central spin model using exact methods
• Spin noise in quantum dot ensembles
• From quantum-mechanical to classical dynamics in the central-spin model
• Spin echo decay at low magnetic fields in a nuclear spin bath

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• Nuclear frequency focusing in periodically pulsed semiconductor quantum dots described by infinite classical central spin models
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• Truncated Wigner approximation for the bosonic model of large spin baths
• Influence of quadrupolar interaction on NMR spectroscopy