Article

# Exact ground states for the four-electron problem in a Hubbard ladder

Philosophical Magazine (Impact Factor: 1.43). 05/2006; 86(13-14):1997. DOI: 10.1080/14786430500070347

Source: arXiv

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**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 [Inline formula] in which the ground state [Inline formula] is placed, than deduces [Inline formula] by exact diagonalization in [Inline formula]. The small subspace is obtained by the repeated application of the Hamiltonian [Inline formula] on a carefully chosen starting wave vector describing the most interacting particle configuration, and the wave vectors resulting from the application of [Inline formula], 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 [Inline formula]. The diagonalization inside [Inline formula] provides an incomplete image of the low lying part of the excitation spectrum, but provides the exact [Inline formula]. Once the exact ground state is obtained, its properties can be easily analysed. The [Inline formula] is found always as a singlet state whose energy, interestingly, saturates in the [Inline formula] 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.Philosophical Magazine 04/2014; 94(19). DOI:10.1080/14786435.2014.904059 · 1.43 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We investigate the ground state phase diagram of the two dimensional Extended Hubbard Model (EHM) with more than Nearest-Neighbor (NN) interactions for finite size system at low concentration. This EHM is solved analytically for finite square lattice at one-eighth filling. All eigenvalues and eigenvectors are given as a function of the on-site repulsion energy U and the off-site interaction energy Vij. The behavior of the ground state energy exhibits the emergence of phase diagram. The obtained results clearly underline that interactions exceeding NN distances in range can significantly influence the emergence of the ground state conductor-insulator transition.International Journal of Modern Physics B 11/2012; 26(29):50156-. DOI:10.1142/S0217979212501561 · 0.46 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Quadratic operators are used in transforming the model Hamiltonian of one correlated and dispersive band in a unique positive semidefinite form coopting both the kinetic and interacting parts of the . The expression is used in deducing exact ground states which are minimum energy eigenstates only of the full Hamiltonian. It is shown in this framework that at half-filling, dispersive bands can also provide ferromagnetism in exact terms through correlation effects.Journal of Physics Condensed Matter 08/2007; 19(38):386209. DOI:10.1088/0953-8984/19/38/386209 · 2.22 Impact Factor