Competition between antiferromagnetic and charge density wave order in the half filled Hubbard-Holstein model

TL;DR

This study uses quantum Monte Carlo simulations to explore the competition between antiferromagnetic and charge density wave orders in the half-filled Hubbard-Holstein model, revealing retardation effects delay charge order and suggest a possible metallic phase.

Contribution

It provides a detailed analysis of how retardation effects influence the competition between AFM and CDW, refining the understanding beyond simple effective-U models.

Findings

Retardation effects delay the onset of charge density wave order.

A window exists where neither AFM nor CDW order dominates, indicating a potential metallic phase.

Charge order remains absent even when the effective U becomes negative.

Abstract

We present a determinant quantum Monte Carlo study of the competition between instantaneous on-site Coulomb repulsion and retarded phonon-mediated attraction between electrons, as described by the two dimensional Hubbard-Holstein model. At half filling, we find a strong competition between antiferromagnetism (AFM) and charge density wave (CDW) order. We demonstrate that a simple picture of AFM-CDW competition that incorporates the phonon mediated attraction into an effective-U Hubbard model requires significant refinement. Specifically, retardation effects slow the onset of charge order, so that CDW order remains absent even when the effective U is negative. This delay opens a window where neither AFM nor CDW order is well established, and where there are signatures of a possible metallic phase.