Simple and accurate method for central spin problems

TL;DR

The paper introduces a simple, accurate quantum mechanical method for simulating the spin correlation tensor in central spin problems, outperforming Monte Carlo, Bethe ansatz, and t-DMRG methods in accuracy and scalability.

Contribution

A novel quantum method that provides long-time accurate results for large central spin systems, surpassing existing techniques in efficiency and precision.

Findings

Accurately computes spin correlation tensors over long times

Applicable to larger systems than Bethe ansatz methods

Provides longer simulation times than t-DMRG

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.