Spectral function of a bipolaron coupled to dispersive optical phonons

Abstract

Using an efficient variational exact diagonalization method, we computed the electron removal spectral function within the framework of the Holstein-Hubbard model containing two electrons with opposite spins coupled to dispersive quantum optical phonons. We focus on how the interplay between the electron-phonon coupling and on-site Coulomb repulsion shapes the spectral function, a quantity directly relevant to angle-resolved photoemission spectroscopy (ARPES). Tuning the strengths of the electron-phonon coupling and the Hubbard interaction allows us to examine the evolution of the spectral properties of the system as it crosses over from a bound bipolaron to separate polarons. We find that phonon dispersion plays an important role: It substantially redistributes the spectral weight across the low- and the high-energy features and controls the emergence and the structure of distinct multiphonon continua. In regimes of strong electron-phonon coupling and low Coulomb repulsion, the spectral function exhibits a broad distribution reflecting bound bipolaronic states. Increasing the Coulomb repulsion weakens bipolaron binding, shifts the primary quasiparticle peak closer to polaronic behavior and confines the spectral weight near the Brillouin-zone center. Our results provide a framework for interpreting ARPES measurements in systems where phonon–mediated attraction competes with direct Coulomb repulsion. Published by the American Physical Society 2025