# Competition among Superconducting, Antiferromagnetic, and Charge Orders with Intervention by Phase Separation in the 2D Holstein-Hubbard Model

## TL;DR

This study investigates the complex interplay of superconductivity, antiferromagnetism, and charge order in the 2D Holstein-Hubbard model, revealing how phase separation influences the emergence and optimization of superconducting phases.

## Contribution

It introduces a variational Monte Carlo analysis of competing orders in the Holstein-Hubbard model, highlighting the role of phase separation in superconductivity.

## Key findings

- Intermediate metallic or weakly superconducting phase appears at half filling.
- Superconductivity is enhanced near the phase separation boundary.
- Phase separation regions hinder the development of superconductivity.

## Abstract

Using a variational Monte Carlo method, we study competitions of strong electron-electron and electron-phonon interactions in the ground state of Holstein-Hubbard model on a square lattice. At half filling, an extended intermediate metallic or weakly superconducting (SC) phase emerges, sandwiched by antiferromagnetic and charge order (CO) insulating phases. By the carrier doping into the CO insulator, the SC order dramatically increases for strong electron-phonon couplings, but largely hampered by wide phase separation (PS) regions. Superconductivity is optimized at the border to the PS.