No spin-localization phase transition in the spin-boson model without local field

TL;DR

This paper demonstrates that in the spin-boson model without a local field, there is no quantum phase transition, and the ground state is uniquely characterized by parity, challenging previous claims of phase transitions.

Contribution

The study provides a rigorous proof of the non-degeneracy of the ground state and clarifies that no QPT occurs in this specific model configuration.

Findings

No quantum phase transition in the zero local field spin-boson model.

Ground state is uniquely characterized by parity and parity breaking.

Previous QPT claims are attributed to treatment issues or infrared divergence.

Abstract

We explore the spin-boson model in a special case, i.e., with zero local field. In contrast to previous studies, we find no possibility for quantum phase transition (QPT) happening between the localized and delocalized phases, and the behavior of the model can be fully characterized by the even or odd parity as well as the parity breaking, instead of the QPT, owned by the ground state of the system. Our analytical treatment about the eigensolution of the ground state of the model presents for the first time a rigorous proof of no-degeneracy for the ground state of the model, which is independent of the bath type, the degrees of freedom of the bath and the calculation precision. We argue that the QPT mentioned previously appears due to unreasonable treatment of the ground state of the model or of the infrared divergence existing in the spectral functions for Ohmic and sub-Ohmic dissipations.