Eur. Phys. J. D 46, 375-380 (2008)
https://doi.org/10.1140/epjd/e2007-00300-9

The dynamics of a central spin in quantum Heisenberg XY model

¹ Department of Physics, Shanghai Jiao Tong University, Shanghai, 200240, P.R. China
² Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei, 10617, Taiwan

Corresponding author: ^a yxz@sjtu.edu.cn

Received: 19 March 2007
Revised: 30 August 2007
Published online: 24 October 2007

Abstract

In the thermodynamic limit, we present an exact calculation of the time dynamics of a central spin coupling with its environment at finite temperatures. The interactions belong to the Heisenberg XY type. The case of an environment with finite number of spins is also discussed. To get the reduced density matrix, we use a novel operator technique which is mathematically simple and physically clear, and allows us to treat systems and environments that could all be strongly coupled mutually and internally. The expectation value of the central spin and the von Neumann entropy are obtained.