Phonon spectral function of the one-dimensional Holstein-Hubbard model

TL;DR

This study employs quantum Monte Carlo simulations to analyze the phonon spectral function in the one-dimensional Holstein-Hubbard model, revealing insights into phase transitions, excitation hybridization, and symmetry breaking.

Contribution

It provides the first detailed calculation of the phonon spectral function across different phases, elucidating the nature of excitations and phase transitions in the model.

Findings

Confirmation of a soft-mode Peierls transition in the adiabatic regime

Identification of a central peak indicating long-range order in the Peierls phase

Observation of phonon dispersion renormalization and its suppression in the Mott phase

Abstract

We use the continuous-time interaction expansion (CT-INT) quantum Monte Carlo method to calculate the phonon spectral function of the one-dimensional Holstein-Hubbard model at half-filling. Our results are consistent with a soft-mode Peierls transition in the adiabatic regime, and the existence of a central peak related to long-range order in the Peierls phase. We explain a previously observed feature at small momenta in terms of a hybridization of charge and phonon excitations. Tuning the system from a Peierls to a metallic phase with a nonzero Hubbard interaction suppresses the central peak, but a significant renormalization of the phonon dispersion remains. In contrast, the dispersion is only weakly modified in the Mott phase. We discuss finite-size effects, the relation to the dynamic charge structure factor, as well as additional sum rules and their implications. Finally, we reveal the existence of a discrete symmetry in a continuum field theory of the Holstein model, which is spontaneously broken in the Peierls phase.