Related papers: One dimensional model for doubly degenerate electr…
We study the ground state of the attractive one-dimensional Bose-Hubbard model, and in particular the nature of the crossover between the weak interaction and strong interaction regimes for finite system sizes. Indicator properties like the…
We study the one-dimensional quarter-filled extended Hubbard model with an alternating transfer integral. In the strong-dimerization limit the charge part is described by the quantum Ising model which shows the two-dimensional Ising…
The Bethe ansatz equations of the 1-D SU(3) Hubbard model are systematically derived by diagonalizing the inhomogeneous transfer matrix of the XXX model. We first derive the scattering matrix of the SU(3) Hubbard model through the…
A new dimensional scaling method for the calculation of excited states of multielectron atoms is introduced. By including the principle and orbital quantum numbers in the dimension parameter, we obtain an energy expression for excited…
We present the exact solution of the one-dimensional extended Hubbard model in the atomic limit within the Green's function and equation of motion formalism. We provide a comprehensive and systematic analysis of the model by considering all…
The properties of the ground state and excitations of a four-component Hubbard-like model are studied by the Lieb-Schultz-Mattis approach. It is proven rigorously that the ground state of the model is nondegenerate and excitations are…
The problem of the transition of electron shells of atoms to excited states in the process of neutrinoless double-$\beta$ decay is investigated. This subject is crucial for modeling the energy spectrum of $\beta$-electrons, which is…
The quantum entanglement for the two electrons in the excited states of the helium-like atom/ions is investigated using the two-electron wave functions constructed by the B-spline basis. As a measure of the spatial (electron-electron…
The entanglement spectrum provides crucial information about correlated quantum systems. We show that the study of the block-like nature of the reduced density matrix in number sectors and the partition dependence of the spectrum in finite…
The Bethe-Salpeter amplitude is expanded on a hyperspherical basis, thereby reducing the original 4-dimensional integral equation into an infinite set of coupled 1-dimensional ones. It is shown that this representation offers a highly…
We report a bound state of the one-dimensional two-particle (bosonic or fermionic) Hubbard model with an impurity potential. This state has the Bethe-ansatz form, although the model is nonintegrable. Moreover, for a wide region in parameter…
We use the $C_{4v}$ symmetry group of the 4-site Hubbard model to construct a ground state variational wave function of two- and four interacting electrons. In the limit $U\rightarrow 0$, ground state energies of the two- and four…
The energy level statistics of the Hubbard model for $L \times L$ square lattices (L=3,4,5,6) at low filling (four electrons) is studied numerically for a wide range of the coupling strength. All known symmetries of the model (space, spin…
We introduce a frustrated spin 1/2 Hamiltonian which is an extension of the two dimensional $J_1 - J_2$ Heisenberg model. The ground states of this model are exactly obtained at a first order quantum phase transition between two regions…
The exact ground state of four electrons in an arbitrary large two leg Hubbard ladder is deduced from nine analytic and explicit linear equations. The used procedure is described, and the properties of the ground state are analyzed. The…
We investigate bound state solutions of the 2D Schr\"odinger equation with a dipole potential originating from the elastic effects of a single edge dislocation. The knowledge of these states could be useful for understanding a wide variety…
We continue the study of the $u(2|2)$-supersymmetric extension of the Hubbard model in one dimension. We determine the excitation spectrum at zero temperature even in the sectors where the ground states are $u(2|2)$-descendants of Bethe…
The energy levels of two interacting electrons in a 2D quantum dot confined by a finite Gaussian potential and subjected to a uniform magnetic field perpendicular to the plane of the dot are studied. Analytic results are obtained for the…
We give upper and lower bounds for the ground-state energy of the infinite-U Hubbard model. In two dimensions, using these bounds we are able to rule out the possibility of phase separation between the undoped-insulating state and an…
A general formalism for the study of excitations above equilibrium in Bethe ansatz solvable models is presented. Nonzero temperature expressions for dressed energy, momentum, spin and charge are obtained, and it is found that the dressed…