Fidelities in the spin-boson model

TL;DR

This paper investigates the overlaps between ground states in the Ohmic spin-boson model, linking the problem to integrable hierarchies and analyzing the impact of Anderson orthogonality on the Yang-Baxter structure.

Contribution

It connects the ground state overlap problem in the spin-boson model to the quantization of integrable hierarchies and studies the effects of Anderson orthogonality on integrability.

Findings

Ground state overlaps relate to mKdV/sine-Gordon hierarchy quantization.

Anderson orthogonality influences the Yang-Baxter integrable structure.

The work provides insights into dissipation and decoherence in quantum systems.

Abstract

The spin-boson model (or the dissipative two-state system) is a model for the study of dissipation and decoherence in quantum mechanics. The spin-boson model with Ohmic dissipation is an integrable theory, related to several other integrable systems including the anisotropic Kondo and resonant level models. Here we consider the problem of computing the overlaps between two ground states corresponding to different values of parameters of the Ohmic spin-boson Hamiltonian. We argue that this can be understood as a part of the problem of quantizing the mKdV/sine-Gordon integrable hierarchy. The main objective of this work is to analyze how the Anderson orthogonality affects the Yang-Baxter integrable structure underlying the theory.