# Spin-Orbital Density Wave and a Mott Insulator in a Two-Orbital Hubbard Model on a Honeycomb Lattice

## TL;DR

This study uses DMRG simulations to explore a two-orbital Hubbard model on a honeycomb lattice, revealing a metal-insulator transition, density wave fluctuations, and a potential nonmagnetic Mott insulator phase relevant to twisted bilayer graphene.

## Contribution

It provides the first detailed DMRG analysis of a two-orbital Hubbard model on a honeycomb lattice, uncovering novel density wave phenomena and a possible Mott insulator phase.

## Key findings

- Metal-insulator transition at Uc/t≈2.5-3
- Strong spin/orbital density wave fluctuations near transition
- Possible nonmagnetic Mott insulator at larger U

## Abstract

Inspired by recent discovery of correlated insulating states in twisted bilayer graphene (TBG), we study a two-orbital Hubbard model on the honeycomb lattice with two electrons per unit cell. Based on the real-space density matrix renormalization group (DMRG) simulation, we identify a metal-insulator transition around $U_c/t=2.5\sim3$. In the vicinity of $U_c$, we find strong spin/orbital density wave fluctuations at commensurate wavevectors, accompanied by weaker incommensurate charge density wave (CDW) fluctuations. The spin/orbital density wave fluctuations are enhanced with increasing system sizes, suggesting the possible emergence of long-range order in the two dimensional limit. At larger $U$, our calculations indicate a possible nonmagnetic Mott insulator phase without spin or orbital polarization. Our findings offer new insights into correlated electron phenomena in twisted bilayer graphene and other multi-orbital honeycomb materials.