Quantum critical point of spin-boson model and infrared catastrophe in bosonic bath

TL;DR

This paper proposes an analytic ground state for the spin-boson model that accounts for quantum phase transition and infrared divergence, providing insights into the critical coupling strength where ground state degeneracy changes.

Contribution

It introduces a non-Gaussian ground state solution that extends beyond the Silbey-Harris state and accurately identifies the quantum critical point.

Findings

The proposed ground state has lower energy than previous models.

Infrared divergence is removable below the critical coupling.

The critical coupling matches previous numerical results.

Abstract

An analytic ground state is proposed for the unbiased spin-boson Hamiltonian, which is non-Gaussian and beyond the Silbey-Harris ground state with lower ground state energy. The infrared catastrophe in Ohmic and sub-Ohmic bosonic bath plays an important role in determining the degeneracy of the ground state. We show that the infrared divergence associated with the displacement of the nonadiabatic modes in bath may be removed from the proposed ground state for the coupling $\alpha<\alpha_c$. Then $\alpha_c$ is the quantum critical point of a transition from non-degenerate to degenerate ground state and our calculated $\alpha_c$ agrees with previous numerical results.