Mott Transitions and Staggered Orders in the Three-component Fermionic System: Variational Cluster Approach

TL;DR

This study uses the variational cluster approximation to explore Mott transitions and staggered orders in a three-component fermionic Hubbard model on a 2D lattice, revealing phase behaviors influenced by interaction anisotropy and Fermi surface nesting.

Contribution

It demonstrates the realization of different Mott and ordered states depending on interaction anisotropy and analyzes their energy mechanisms using a variational cluster approach.

Findings

Paired Mott or color-selective Mott states depend on interaction anisotropy.

First-order transition between color-density-wave and color-selective antiferromagnetic states at SU(3) point.

Staggered orders are fragile and depend on Fermi surface nesting.

Abstract

The variational cluster approximation is used to study the ground-state properties and single-particle spectra of the three-component fermionic Hubbard model defined on the two-dimensional square lattice at half filling. First, we show that either a paired Mott state or color-selective Mott state is realized in the paramagnetic system, depending on the anisotropy in the interaction strengths, except around the SU(3) symmetric point, where a paramagnetic metallic state is maintained. Then, by introducing Weiss fields to observe spontaneous symmetry breakings, we show that either a color-density-wave state or color-selective antiferromagnetic state is realized depending on the interaction anisotropy and that the first-order phase transition between these two states occurs at the SU(3) point. We moreover show that these staggered orders originate from the gain in potential energy (or Slater mechanism) near the SU(3) point but originate from the gain in kinetic energy (or Mott mechanism) when the interaction anisotropy is strong. The staggered orders near the SU(3) point disappear when the next-nearest-neighbor hopping parameters are introduced, indicating that these orders are fragile, protected only by the Fermi surface nesting.