The emergence domain of an exact ground state in a non-integrable system: the case of the polyphenylene type of chains

Abstract

A technique based on the transformation in positive semidefinite form of the Hamiltonian (Ĥ) is developed to allow the study of the enlargement possibilities of the emergence domain of a given state. For this reason the calculation of exact ground states for the polyphenylene type of non-integrable chains is performed. Using different exact transcriptions of Ĥ in positive semidefinite form and different solutions of the matching equations, the same type of ground state is deduced in different regions of the parameter space, hence a more global view of its emergence possibilities is obtained. With this procedure an enlarged view of the appearance in the phase diagram of different studied phases can be achieved.

Keywords:

• exact ground states
• polyphenylene
• positive semidefinite operators
• hexagon chains
• strongly correlated systems
• Hubbard models

Acknowledgements

The research of ZG was supported by OTKA-K-100288, TAMOP-4.2.1/B-09/ 1/KONV-2010-0007 research contracts and the Alexander von Humboldt Foundation. The research of RT was funded by TAMOP-4.2.2/B-10/1-2010-0024. We note that both TAMOP subprojects are co-financed by the EU and European Social Fund.

Notes

Note

1. Note that as defined in the first line of (26), the parameter γ is composite, i.e. it is a complicated expression of different Ĥ parameters. But even in this case, by letting t ₁ → ∞ (t ₁ → 0), one easily achieves γ < 1 (γ > 1), respectively.