Rigorous results on the ground state of the attractive SU($N$) Hubbard model

TL;DR

This paper provides rigorous theoretical results on the ground state properties of the attractive SU(N) Hubbard model, including degeneracy, fermion number, and symmetry, applicable to bipartite lattices of any dimension.

Contribution

The authors prove three theorems characterizing the ground state properties of the attractive SU(N) Hubbard model on bipartite lattices, regardless of translation invariance.

Findings

Ground state degeneracy characterized

Fermion number determined

Charge density wave order when sublattice sizes differ significantly

Abstract

We study the attractive SU($N$) Hubbard model with particle-hole symmetry. The model is defined on a bipartite lattice with the number of sites $N_A$ $(N_B)$ in the $A$ $(B)$ sublattice. We prove three theorems that allow us to identify the basic ground-state properties: the degeneracy, the fermion number, and the SU($N$) quantum number. We also show that the ground state exhibits charge density wave order when $|N_A-N_B|$ is macroscopically large. The theorems hold for a bipartite lattice in any dimension, even without translation invariance.