Ground-state properties of sub-Ohmic spin-boson model with simultaneous diagonal and off-diagonal coupling

Abstract

By employing a variational approach, the density matrix renormalization group (DMRG), the exact diagonalization, and symmetry and mean-field analyses, the ground-state properties of the two-bath spin-boson model with simultaneous diagonal and off-diagonal coupling are systematically studied in the sub-Ohmic regime. A quantum phase transition from a doubly degenerate “localized phase” to the other doubly degenerate “delocalized phase” is uncovered. Via the multi-D1 Ansatz as the variational wave function, transition points are determined accurately, consistent with the results from DMRG and exact diagonalization. An effective spatial dimension deff=2.37(6) is then estimated, which is found to be compatible with the mean-field prediction. Furthermore, the quantum phase transition is inferred to be of first order for the baths described by a continuous spectral density function. In the single-mode case, however, the transition is softened.