Separation-dependent localization in a two-impurity spin-boson model

TL;DR

This paper investigates how the transition from delocalized to localized states in a two-impurity spin-boson model depends on system parameters, revealing a variable crossover point influenced by impurity separation and external fields.

Contribution

It introduces a variational approach to analyze the crossover in a two-impurity spin-boson model, highlighting the dependence of the critical coupling on impurity separation and external fields, unlike the single spin case.

Findings

Crossover occurs between α_c=0.5 and 1 depending on parameters.

System-environment entanglement signals the crossover.

Qualitative features align with a dissipative two-spin transverse Ising model.

Abstract

Using a variational approach we investigate the delocalized to localized crossover in the ground state of an Ohmic two-impurity spin-boson model, describing two otherwise non-interacting spins coupled to a common bosonic environment. We show that a competition between an environment-induced Ising spin interaction and externally applied fields leads to variations in the system-bath coupling strength, $\alpha_c$, at which the delocalized-localized crossover occurs. Specifically, the crossover regime lies between $\alpha_c=0.5$ and $\alpha_c=1$ depending upon the spin separation and the strength of the transverse tunneling field. This is in contrast to the analogous single spin case, for which the crossover occurs (in the scaling limit) at fixed $\alpha_c\approx1$. We also discuss links between the two-impurity spin-boson model and a dissipative two-spin transverse Ising model, showing that the latter possesses the same qualitative features as the Ising strength is varied. Finally, we show that signatures of the crossover may be observed in single impurity observables, as well as in the behaviour of the system-environment entanglement.