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arXiv:cond-mat/9503122 · Physical Review Letters

Exact Ground States of Generalized Hubbard Models

Jan De Boer A, Andreas Schadschneider

Published Dec 4, 1995• 76 citations
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Abstract

We present a simple method for the construction of exact ground states of generalized Hubbard models in arbitrary dimensions. This method is used to derive rigorous criteria for the stability of various ground state types, like the $\ensuremath{\eta}$-pairing state, or N\'eel and ferromagnetic states. Although the approach presented here is much simpler than the ones commonly used, it yields better bounds for the region of stability.

DOI
10.1103/physrevlett.75.4298

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We present a simple method for the construction of exact ground states of generalized Hubbard models in arbitrary dimensions. This method is used to derive rigorous criteria for the stability of various ground state types, like the \ensuremathη\ensuremath{\eta}\ensuremathη-pairing state, or N'eel and ferromagnetic states. Although the approach presented here is much simpler than the ones commonly used, it yields better bounds for the region of stability.
The ground-state phase diagram of the extended Hubbard model containing nearest- and next-to-nearest-neighbor interactions is investigated in the thermodynamic limit using an exact method. It is found that taking into account local correlations and adding next-to-nearest-neighbor interactions both have significant effects on the position of the phase boundaries. Improved stability domains for the $\ensuremath{\eta}$-pairing state and for the fully saturated ferromagnetic state at half-filling have been constructed. The results show that these states are the ground states for model Hamiltonians with realistic values of the interaction parameters.
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 Néel ordered states on the dual lattices. We demonstrate this idea in the one-dimensional chain and higher-dimensional lattices such as the Kagomé lattice, and determine parameter regions of the exact ground states.