Optimum ground states of generalized Hubbard models with next-nearest neighbour interaction

TL;DR

This paper analyzes the stability of ground states in generalized Hubbard models with next-nearest neighbor interactions, providing exact bounds and exploring how additional interactions influence stability regions.

Contribution

It introduces an approach to determine exact stability bounds for ground states in complex Hubbard models, including effects of extended interactions.

Findings

Exact lower bounds for stability regions of specific ground states.

Larger clusters improve bounds for models with only nearest neighbor interactions.

Next-nearest neighbor interactions can expand or contract stability regions.

Abstract

We investigate the stability domains of ground states of generalized Hubbard models with next-nearest neighbour interaction using the optimum groundstate approach. We focus on the $\eta$-pairing state with momentum P=0 and the fully polarized ferromagnetic state at half-filling. For these states exact lower bounds for the regions of stability are obtained in the form of inequalities between the interaction parameters. For the model with only nearest neighbour interaction we show that the bounds for the stability regions can be improved by considering larger clusters. Additional next-nearest neighbour interactions can lead to larger or smaller stability regions depending on the parameter values.