An Efficient Algorithm for Simulating the Real-Time Quantum Dynamics of a Single Spin-1/2 Coupled to Specific Spin-1/2 Baths

• Published in: Journal of physics. Conference series Vol. 402; no. 1; pp. 12019 - 17
• Main Authors: Novotny, M A, Guerra, M, De Raedt, H, Michielsen, K, Jin, F
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 20.12.2012
• Subjects: Algorithms; Couplings; Density; Entropy; Hilbert space; Joining; Mathematical analysis; Physics; Real time; Spin dynamics; Time dependence; Vectors (mathematics)
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/402/1/012019

An efficient algorithm for the computation of the real-time dependence of a single quantum spin-1/2 coupled to a specific set of quantum spin-1/2 baths is presented. The specific spin baths have couplings only with the spin operators Sx between bath spins and the central spin. We calculate spin expectation values, the quantum purity, the von Neumann entropy, and the off-diagonal components of the reduced density matrix for the central spin once the bath spins have been traced out. The algorithm does not require the storage of any vector larger than of size 2, even though the size of the Hilbert space is 2N+1, where N is the number of bath spins. Results are presented for the central spin connected to different sizes and types of spin baths, and for different initial states for the central spin and for the bath spins. Results are also compared to those for more general baths.