Correlation Effects in a Simplified Bilayer Two-Orbital Hubbard Model at Half Filling

TL;DR

This study uses quantum Monte Carlo simulations to explore the phase diagram and correlation effects in a simplified bilayer two-orbital Hubbard model, revealing a transition from a weakly insulating to an antiferromagnetic Mott insulator phase relevant to high-temperature superconductivity in nickelates.

Contribution

It provides the first detailed numerical analysis of correlation-driven phase transitions in a bilayer two-orbital Hubbard model at half filling, connecting to experimental findings in La$_3$Ni$_2$O$_7$.

Findings

Identification of a phase transition at U/t_1^x ≈ 4.15.

Observation of a nonmagnetic weakly insulating phase at weak interactions.

Correlation effects explain features observed in ARPES experiments.

Abstract

Motivated by the discovery of high-temperature superconductivity in bilayer nickelate La$_3$Ni$_2$O$_7$ under pressure, we investigate the ground-state phase diagram and correlation effects using determinant quantum Monte Carlo simulations in a simplified bilayer two-orbital Hubbard model at half filling. Our results reveal the emergence of a nonmagnetic weakly insulating phase at weak on-site Hubbard interactions, transitioning to an antiferromagnetic Mott insulating phase as the interaction strength exceeds a critical value $U/t_1^x\approx 4.15$. This phase transition is consistent with the 3D O(3) Heisenberg universality class. Additionally, we analyze dynamical properties such as the single-particle spectral function and dynamic spin structure factor. The pronounced inter-layer correlation of $d_{3z^2-r^2}$ orbitals results in a downward trend and an extended flatness in the $\gamma$ band, mirroring the angle-resolved photoemission spectroscopy findings under ambient pressure. Our numerical results provide important clues for understanding the strong correlation effects in La$_3$Ni$_2$O$_7$.