Many-body theory of spin bath dynamics for qubit decoherence*

We have developed a cluster correlation expansion (CCE) theory for the many-body dynamics of a finite-size spin bath in a time scale relevant to decoherence of a center spin or a qubit embedded in the bath [1]. In terms of the linked cluster expansion, a cluster correlation term is the infinite summation of all the linked diagrams with all the spins in the cluster flip-flopped. The lowest order of the cluster correlation corresponds to the pair-correlation approximation developed previously [2]. In the thermodynamics limit, the CCE reduces to the standard cluster expansion. The CCE is especially useful for studying multi-spin coherence in small spin baths such as NV centers in diamonds and molecular magnets, where the cluster expansion fails to converge to the exact solution. \\[4pt] [1] W. Yang and R. B. Liu, Phys. Rev. B \textbf{78}, 085315 (2008).\\[0pt] [2] W. Yao, R. B. Liu and L. J. Sham, Phys. Rev. B \textbf{74}, 195301 (2006).