Two-dimensional Hubbard-Holstein bipolaron

TL;DR

This study uses diagrammatic Monte Carlo simulations to explore bipolaron states in a 2D Hubbard-Holstein model, revealing a sharp transition between weakly and strongly bound bipolarons and discovering a new nearest-neighbor bipolaron state.

Contribution

It provides a detailed phase diagram of bipolaron states in the 2D Hubbard-Holstein model using an exact numerical method without artificial approximations.

Findings

Identified a sharp transition from light to heavy bipolarons at specific electron-phonon coupling.

Discovered a new bipolaron state with polarons on neighboring sites at large U.

Mapped the phase diagram showing different bipolaron regimes.

Abstract

We present a diagrammatic Monte Carlo study of the properties of the Hubbard-Holstein bipolaron on a two-dimensional square lattice. With a small Coulomb repulsion, U, and with increasing electron-phonon interaction, and when reaching a value about two times smaller than the one corresponding to the transition of light polaron to heavy polaron, the system suffers a sharp transition from a state formed by two weakly bound light polarons to a heavy, strongly bound on-site bipolaron. Aside from this rather conventional bipolaron a new bipolaron state is found for large U at intermediate and large electron-phonon coupling, corresponding to two polarons bound on nearest-neighbor sites. We discuss both the properties of the different bipolaron states and the transition from one state to another. We present a phase diagram in parameter space defined by the electron-phonon coupling and U. Our numerical method does not use any artificial approximation and can be easily modified to other bipolaron models with longer range electron-phonon and/or electron-electron interaction.