Symmetry and the critical phase of the two-bath spin-boson model: Ground-state properties

TL;DR

This paper introduces a new variational wave function to study the ground state of a complex spin-boson model, revealing symmetry breaking and accurately determining the phase boundary in the sub-Ohmic regime.

Contribution

The study develops the multi-D1 Ansatz for analyzing the spin-boson model with diagonal and off-diagonal couplings, providing new insights into symmetry breaking and phase transition boundaries.

Findings

Symmetry breaking occurs along the quantum phase transition.

The phase boundary is precisely determined using symmetry parameters.

The critical spectral exponent s* is estimated as 0.49(1).

Abstract

A generalized trial wave function termed as the "multi-D1 Ansatz" has been developed to study the ground state of the spin-boson model with simultaneous diagonal and off-diagonal coupling in the sub-Ohmic regime. Ground-state properties including the energy and the spin polarization are investigated, and the results are consistent with those from the exact diagonalization and density matrix renormalization group approaches for the cases involving two oscillators and two baths described by a continuous spectral density function. Breakdown of the rotational and parity symmetries along the continuous quantum phase transition separating the localized phase from the critical phase has been uncovered. Moreover, the phase boundary is determined accurately with the corresponding symmetry parameters of the rotational and parity symmetries. A critical value of the spectral exponent s* = 0.49(1) is predicted in the weak coupling limit, which is in agreement with the mean-field prediction of 1/2, but much smaller than the earlier literature estimate of 0.75(1).