Ground-state properties of the two-site Hubbard-Holstein model: an exact solution

TL;DR

This paper provides an exact analysis of the ground-state properties of the two-site Hubbard-Holstein model, revealing detailed insights into bipolaron behavior, entanglement, and crossover phenomena across coupling regimes.

Contribution

It introduces an exact solution approach using extended phonon coherent states to study bipolaron states in the two-site Hubbard-Holstein model.

Findings

Maximum bipartite entanglement in strong coupling regime

Crossover from two-site to single-site bipolaron is abrupt and shifts with Coulomb repulsion

Ground-state energy and double occupancy are quantitatively characterized

Abstract

We revisit the two-site Hubbard-Holstein model by using extended phonon coherent states. The nontrivial singlet bipolaron is studied exactly in the whole coupling regime. The ground-state (GS) energy and the double occupancy probability are calculated. The linear entropy is exploited successfully to quantify bipartite entanglement between electrons and their environment phonons, displaying a maximum entanglement of the singlet-bipolaron in strong coupling regime. A dramatic drop in the crossover regime is observed in the GS fidelity and its susceptibility. The bipolaron properties is also characterized classically by correlation functions. It is found that the crossover from a two-site to single-site bipolaron is more abrupt and shifts to a larger electron-phonon coupling strength as electron-electron Coulomb repulsion increases.