Sign-Free Determinant Quantum Monte Carlo Study of Excitonic Density Orders in a Two-Orbital Hubbard-Kanamori Model

TL;DR

This study uses sign-free determinant quantum Monte Carlo to explore excitonic density orders in a two-orbital Hubbard-Kanamori model, revealing how Hund's coupling influences the emergence and nature of these orders.

Contribution

It provides the first sign-problem-free quantum Monte Carlo analysis of excitonic orders in a multiorbital model including Hund's coupling effects.

Findings

Negative Hund's exchange promotes excitonic density order.

Positive Hund's coupling favors spin-triplet excitonic phases.

Competition exists between anti-ferro-orbital and excitonic orders.

Abstract

While excitonic instabilities in multiorbital systems recently have come under scrutiny in a variety of transition-metal compounds, understanding emergence of these instabilities from strong electronic interactions has remained a challenge. Here, we present a sign-problem-free determinant quantum Monte Carlo study of excitonic density orders in a half-filled two-orbital Hubbard-Kanamori model with broken orbital degeneracy, which accounts for the role of Hund's coupling in transition-metal compounds. For strong inverted (negative) Hund's exchange, we find numerical evidence for the emergence of excitonic density order, with competition between anti-ferro-orbital order and $\mathbf{Q} = (\pi,\pi)$ excitonic density order as a function of orbital splitting and Hund's coupling. While inverted Hund's coupling stabilizes a spin-singlet excitonic density phase for weak orbital splitting, positive Hund's coupling favors a spin-triplet excitonic density phase.