# Competing Charge and Magnetic Order in Fermionic Multi-Component Systems

## TL;DR

This paper explores the complex interplay of charge and magnetic orders in a three-component fermionic Hubbard model on a triangular lattice, revealing a rich phase diagram with multiple intermediate phases influenced by interaction strength and potential.

## Contribution

It introduces a detailed phase diagram for the SU(3) Hubbard model with a staggered potential, highlighting the competition between charge and magnetic orders and the emergence of novel intermediate phases.

## Key findings

- Destabilization of band insulator into Mott insulator with increasing U
- Identification of multiple intermediate phases depending on U and Δ
- Observation of competition between charge and magnetic orders in multi-component systems

## Abstract

We consider the fermionic SU($3$) Hubbard model on the triangular lattice in the presence of a three-sublattice staggered potential which provides the possibility to investigate the competition of charge and magnetic order in three-component systems. We show that depending on the strength of the staggered potential $\Delta$, the Hubbard interaction $U$ destabilizes the band insulator (BI) at small $U$ into the Mott insulator (MI) at large $U$ in three different ways with different intermediate phases. This leads to a rich phase diagram in the $U$-$\Delta$ plane. Our results indicate that multi-component systems show not only exotic states in the Mott regime as has been considered previously, but also interesting competition between charge and magnetic orders.