Exact ground state for the four-electron problem in a 2D finite honeycomb lattice

Abstract

Working in a subspace with dimensionality much smaller than the dimension of the full Hilbert space, we deduce exact four-particle ground states in 2D samples containing hexagonal repeat units and described by Hubbard type of models. The procedure identifies first a small subspace in which the ground state is placed, than deduces by exact diagonalization in . The small subspace is obtained by the repeated application of the Hamiltonian on a carefully chosen starting wave vector describing the most interacting particle configuration, and the wave vectors resulting from the application of , till the obtained system of equations closes in itself. The procedure which can be applied in principle at fixed but arbitrary system size and number of particles is interesting on its own since it provides exact information for the numerical approximation techniques which use a similar strategy, but apply non-complete basis for . The diagonalization inside provides an incomplete image of the low lying part of the excitation spectrum, but provides the exact . Once the exact ground state is obtained, its properties can be easily analysed. The is found always as a singlet state whose energy, interestingly, saturates in the limit. The unapproximated results show that the emergence probabilities of different particle configurations in the ground state presents ‘Zittern’ (trembling) characteristics which are absent in 2D square Hubbard systems. Consequently, the manifestation of the local Coulomb repulsion in 2D square and honeycomb types of systems presents differences, which can be a real source in the differences in the many-body behaviour.

Keywords:

• strongly correlated electrons
• Hubbard model
• nanomaterials

Acknowledgments

Z.G. kindly acknowledges financial support provided by Alexander von Humboldt Foundation, OTKA-K-100288 (Hungarian Research Funds for Basic Research) and TAMOP 4.2.2/A-11/1/KONV-2012-0036 (co-financed by EU and European Social Fund).

Notes

1 One notes that in the Appendix 1, Equation (A1) of Ref. [24], four misprint have been observed, namely: (a) in the right side of the equation for , instead of , must be written, (b) in the right side of the equation for , instead of , must be written, (c) in the right side of the equation for , instead of , must be written, (d) in the right side of the equation for , instead of , must be written.

2 The order of magnitude differences between Figures 10 and 11 can be attributed to the different number of components in the vector in the hexagonal and square system cases.