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

TL;DR

This study investigates the ground state properties of the sub-Ohmic spin-boson model with combined diagonal and off-diagonal couplings, revealing a novel first-order quantum phase transition and accurately determining transition points.

Contribution

It introduces a comprehensive analysis using multiple methods to uncover a new quantum phase transition in a complex spin-boson system with simultaneous couplings.

Findings

Discovery of a new quantum phase transition from localized to delocalized phases.

Accurate determination of transition points using variational and numerical methods.

Estimation of an effective spatial dimension consistent with mean-field theory.

Abstract

By employing the variational approach, density matrix renormalization group (DMRG), exact diagonalization as well as 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 novel 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 $d_{eff} = 2.37(6)$ 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 case of single mode, however, the transition is softened.