Spin Path Integrals, Berry phase, and the Quantum Phase Transition in the sub-Ohmic Spin-boson Model

TL;DR

This paper explores how the Berry phase influences the quantum critical behavior in the sub-Ohmic spin-boson model, revealing that the path integral formulation involves a Berry phase which affects the nature of quantum phase transitions.

Contribution

It provides a detailed analysis of the spin path integral representation, highlighting the role of the Berry phase in the quantum-critical properties of the spin-boson model with anisotropy.

Findings

Berry phase appears in the continuum limit of the path integral.

The effective action deviates from the Ginzburg-Landau-Wilson form due to the Berry phase.

Implications for quantum criticality in spin models are discussed.

Abstract

The quantum critical properties of the sub-Ohmic spin-1/2 spin-boson model and of the Bose-Fermi Kondo model have recently been discussed controversially. The role of the Berry phase in the breakdown of the quantum-to-classical mapping of quantum criticality in the spin-isotropic Bose-Fermi Kondo model has been discussed previously. In the present article, some of the subtleties underlying the functional integral representation of the spin-boson and related models with spin anisotropy are discussed. To this end, an introduction to spin coherent states and spin path integrals is presented with a focus on the spin-boson model. It is shown that, even for the Ising-anisotropic case as in the spin-boson model, the path integral in the continuum limit in the coherent state representation involves a Berry phase term. As a result, the effective action for the spin degrees of freedom does not assume the form of a Ginzburg-Landau-Wilson functional. The implications of the Berry-phase term for the quantum-critical behavior of the spin-boson model are discussed. The case of arbitrary spin is also considered.