Ground state and dynamics of the biased dissipative two-state system: Beyond variational polaron theory

TL;DR

This paper introduces an improved ground-state ansatz for the biased Ohmic spin-boson model that accurately captures the crossover behavior and aligns well with Bethe-ansatz results, enabling advanced dynamics analysis.

Contribution

It presents a novel ground-state ansatz surpassing variational methods, accurately modeling crossover behavior and facilitating non-perturbative dynamics analysis.

Findings

Accurately models the smooth crossover in ground-state magnetization.

Provides lower energy estimates in the crossover region.

Aligns well with Bethe-ansatz predictions.

Abstract

We propose a ground-state ansatz for the Ohmic spin-boson model that improves upon the variational treatment of Silbey and Harris for biased systems in the scaling limit. In particular, it correctly captures the smooth crossover behaviour expected for the ground-state magnetisation when moving between the delocalised and localised regimes of the model, a feature that the variational treatment is unable to properly reproduce, while it also provides a lower ground-state energy estimate in the crossover region. We further demonstrate the validity of our intuitive ground-state by showing that it leads to predictions in excellent agreement with those derived from a non-perturbative Bethe-ansatz technique. Finally, recasting our ansatz in the form of a generalised polaron transformation, we are able to explore the dissipative two-state dynamics beyond weak system-environment coupling within an efficient time-local master equation formalism.