On the spin--boson model with a sub--Ohmic bath

TL;DR

This paper investigates the spin--boson model with a sub--Ohmic bath using infinitesimal unitary transformations, revealing a zero-temperature phase transition and algebraic decay of correlation functions, contrasting previous findings.

Contribution

It provides an explicit expression for the renormalized level spacing and clarifies the nature of the phase transition in the sub--Ohmic spin--boson model.

Findings

Identifies a zero-temperature transition from untrapped to trapped state.

Derives an explicit formula for the renormalized level spacing.

Shows algebraic decay of equilibrium correlation functions at zero temperature.

Abstract

We study the spin--boson model with a sub--Ohmic bath using infinitesimal unitary transformations. Contrary to some results reported in the literature we find a zero temperature transition from an untrapped state for small coupling to a trapped state for strong coupling. We obtain an explicit expression for the renormalized level spacing as a function of the bare papameters of the system. Furthermore we show that typical dynamical equilibrium correlation functions exhibit an algebaric decay at zero temperature.