Exact Plaquette-Ordered Ground States in the Generalized Hubbard Model in Arbitrary Dimensions

TL;DR

This paper demonstrates the existence of exact plaquette-ordered ground states in the generalized Hubbard model across arbitrary dimensions, using Hamiltonian decomposition into projection operators, with applications to various lattice structures.

Contribution

It introduces a method to find exact ground states in the Hubbard model with site-off-diagonal interactions for any dimension, expanding understanding of ordered states.

Findings

Exact plaquette-ordered ground states exist in the Hubbard model with off-diagonal interactions.

The method applies to one-dimensional chains and complex lattices like Kagomé.

Parameter regions for these ground states are explicitly determined.

Abstract

We show the existance of the exact plaquette-ordered ground states of the Hubbard model including site-off-diagonal interactions in arbitrary dimensions, by decomposing the Hamiltonian as sum of products of projection operators for each spin sector. The obtatined exact ground states are interpreted as N\'eel ordered states on the dual lattices. We demonstrate this idea in the one-dimensional chain and higher-dimensional lattices such as the Kagom\'e lattice, and determine parameter regions of the exact ground states.