Exact calculation of the two-electron interaction in the ground state of the Hubbard model

Analysis of the New Unrestricted Hartree‐Fock Vortex Solution of the Hubbard Hamiltonian in Two‐Dimensional Systems A Small‐Cluster Study

“…5 on-site Hubbard repulsion, electrons tend to separate as much as possible to avoid collisions. The same conclusion was reached in [7] through the study of the pair correlation function in very large clusters. We have extended the study of two correlated electrons to larger clusters (up to 13 x 13).…”

“…Taking full account of symmetry and spin conservation the problem reduces to the diagonalization of small matrices. Our procedure is closely related to the one employed by Chen and Mei [7] to solve the same 46* problem, the main difference between both approaches being the use of diagonalization to get the coefficients of the singlet wave functions instead of minimization in [7]. In this way, we have obtained exact wave functions and energies for 3 x 3 and 4 x 4 clusters.…”

“…Taking full account of symmetry and spin conservation the problem reduces to the diagonalization of small matrices. Our procedure is closely related to the one employed by Chen and Mei [7] to solve the same 46* Fig. 3 for a 4 x 4 cluster of the two-dimensional square lattice.…”

Exact ground states for the four-electron problem in a two-dimensional finite Hubbard square system

“…In order to enhance further developments and enlighten further creative thinking, we provide, explicitly in Appendix A, the equations generating the ground state, together with the explicit form of the base vectors providing the ground state (see figures [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], hence describing the Hilbert space region in which this is placed. We mention that if the base vectors are defined only through the operation T, without subtracting two T components as shown in figures 4-18, a system containing 176 equations arises.…”

A Highly Simplified Correlated Variational Study of the Singlet-Triplet Transition in Quantum Dots embedded in Kagome Lattice

“…If one consider first only the singlet states, that is, states in which the pair of electrons have opposite spins, \iaja,kaja >, one gets a 36 x 36 matrix which is then diagonahzed to obtain the ground state energy. The corresponding eigenvector is used to construct the ground state wavefunction which is then used as the trial wavefunction in obtaining an expression in matrix form for the variational ground state energy for the t-U model [16]. It is then straightforward to include triplet states to the wavefunction and the V and J interactions leading to a general expression in matrix form for the variational ground state energy, E, for the t-U-V-J model.…”