Simple and accurate method for central spin problems

Abstract

We describe a simple quantum mechanical method that can be used to obtain accurate numerical results over long time scales for the spin correlation tensor of an electron spin that is hyperfine coupled to a large number of nuclear spins. This method does not suffer from the statistical errors that accompany a Monte Carlo sampling of the exact eigenstates of the central spin Hamiltonian obtained from the algebraic Bethe ansatz, or from the growth of the truncation error with time in the time-dependent density matrix renormalization group (t-DMRG) approach. As a result, it can be applied to larger central spin problems than the algebraic Bethe ansatz, and for longer times than the t-DMRG algorithm. It is therefore an ideal method to use to solve central spin problems, and we expect that it will also prove useful for a variety of related problems that arise in a number of different research fields.

arXiv commentArticle: 5 pages, 5 figures Supplementary material: 15 pages, 6 figures

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• Separable and entangled states in the high-spin XX central spin model
• Dynamic mean-field theory for dense spin systems at infinite temperature
• Non-Gaussian dynamics of quantum fluctuations and mean-field limit in open quantum central spin systems
• Interplay of spin mode locking and nuclei-induced frequency focusing in quantum dots
• Quantum mechanical spin dynamics of a molecular magnetoreceptor
• Understanding the dynamics of randomly positioned dipolar spin ensembles
• Long-time memory effects in a localizable central spin problem
• Probability Thermodynamics and Probability Quantum Field
• Dissipative evolution of a two-level system through a geometry-based classical mapping
• Finding the Dynamics of an Integrable Quantum Many-Body System via Machine Learning
• Numerically exact quantum dynamics with tensor networks: Predicting the decoherence of interacting spin systems
• Truncated Wigner approximation for the bosonic model of large spin baths