# Competing phases and orbital-selective behaviors in the two-orbital Hubbard-Holstein model

## TL;DR

This study explores how electron-electron and electron-phonon interactions influence phase behavior in a two-orbital Hubbard-Holstein model, revealing an orbital-selective Peierls insulator and emphasizing the importance of considering e-ph interactions.

## Contribution

It introduces the orbital-selective Peierls insulating phase and analyzes the interplay between e-e and e-ph interactions using dynamical mean field theory.

## Key findings

- E-ph interaction modifies the phase diagram significantly.
- Discovery of an orbital-selective Peierls insulating phase.
- Hund's coupling affects the transition to the OSPI.

## Abstract

We study the interplay between the electron-electron (e-e) and the electron-phonon (e-ph) interactions in the two-orbital Hubbard-Holstein model at half filling using the dynamical mean field theory. We find that the e-ph interaction, even at weak couplings, strongly modifies the phase diagram of this model and introduces an orbital-selective Peierls insulating phase (OSPI) that is analogous to the widely studied orbital-selective Mott phase (OSMP). At small e-e and e-ph coupling, we find a competition between the OSMP and the OSPI, while at large couplings, a competition occurs between Mott and charge-density-wave (CDW) insulating phases. We further demonstrate that the Hund's coupling influences the OSPI transition by lowering the energy associated with the CDW. Our results explicitly show that one must be cautious when neglecting the e-ph interaction in multiorbital systems, where multiple electronic interactions create states that are readily influenced by perturbing interactions.