Equilibrium Correlation Functions of the Spin-Boson Model with Sub-Ohmic Bath

TL;DR

This paper develops a unified flow equation approach to compute equilibrium correlation functions of the spin-boson model across different bath types, including sub-Ohmic, Ohmic, and super-Ohmic, with finite bias.

Contribution

It introduces a comprehensive truncation scheme and a universal flow equation framework for analyzing the spin-boson model with various bath spectral densities.

Findings

Successfully computes equilibrium correlation functions for all bath types.

Identifies a universal attractor in the Hamiltonian flow.

Handles finite bias within the flow equation approach.

Abstract

The spin-boson model is studied by means of flow equations for Hamiltonians. Our truncation scheme includes all coupling terms which are linear in the bosonic operators. Starting with the canonical generator $\eta_c=[H_0,H]$ with $H_0$ resembling the non-interacting bosonic bath, the flow equations exhibit a universal attractor for the Hamiltonian flow. This allows to calculate equilibrium correlation functions for super-Ohmic, Ohmic and sub-Ohmic baths within a uniform framework including finite bias.