Renormalization of spectra by phase competition in the half-filled Hubbard-Holstein model

TL;DR

This study uses quantum Monte Carlo simulations to analyze how electron-electron and electron-phonon interactions influence spectral functions and phase transitions in the half-filled 2D Hubbard-Holstein model, revealing the emergence of metallic phases.

Contribution

It provides a detailed analysis of spectral renormalizations due to combined interactions, highlighting their role in phase transitions and metallicity in strongly correlated systems.

Findings

Spectral functions evolve between insulating and metallic phases with interaction tuning.

Phonon spectra soften and become momentum-dependent near charge density wave phase.

Coexistence of interactions suppresses low-energy renormalization, enabling metallic behavior.

Abstract

We present electron and phonon spectral functions calculated from determinant quantum Monte Carlo simulations of the half-filled two-dimensional Hubbard-Holstein model on a square lattice. By tuning the relative electron-electron ($e$-$e$) and electron-phonon ($e$-$ph$) interaction strengths, we show the electron spectral function evolving between antiferromagnetic insulating, metallic, and charge density wave insulating phases. The phonon spectra concurrently gain a strong momentum dependence and soften in energy upon approaching the charge density wave phase. In particular, we study how the $e$-$e$ and $e$-$ph$ interactions renormalize the spectra, and analyze how the interplay of these interactions influence the spectral renormalizations. We find that the presence of both interactions suppresses the amount of renormalization at low energy, thus allowing the emergence of a metallic phase. These findings demonstrate the importance of considering the influence of multiple interactions in spectroscopically determining any one interaction strength in strongly correlated materials.