Effective Hamiltonian for the motion of holes in the Hubbard-Anderson model

The motion of (interacting) holes in the Hubbard-Anderson model for high-Tc superconductivity is translated into the motion of (coupled) spinless fermions. The entities responsible for the coupling are localized spin excitations and are described by bosons. The new description shows resemblance with the BCS description of electrons and photons of the ¿classical¿ superconductors

Symmetry breaking in the Anderson-Hubbard model

The Anderson-Hubbard (A-H) model with one or two holes and with periodic boundary conditions on a 4Mx 4N square lattice is considered. On grounds of an intuitive generalization of Marshall's theorem we split the A-H Hamiltonian (HA−H) into a zeroth order term (H0) and a perturbation term (H'). With H0 we construct unfrustrated states: the zeroth order approximation of the degenerate ground state (GS). The one-hole system has a four-fold symmetry broken H0-GS with k = (π/2, ±π/2), (-π/2, ±π/2). Group theory shows that this symmetry breaking (SB) may be stable if H' is taken into account. For the two-hole system we derive candidates for the H0-GS with the corresponding good quantum numbers k and total spin S. Here we find no SB or a two-fold SB: again, this result may hold for the complete HA−H. Second order perturbation calculation possibly describes an effective coupling of two holes

The two-hole ground state of the Hubbard-Anderson model, approximated by a variational RVB-type wave function

In this paper the Hubbard-Anderson model on a square lattice with two holes is studied. The ground state (GS) is approximated by a variational RVB-type wave function. The holes interact by exchange of a localized spin excitation (SE), which is created or absorbed if a hole moves to a nearest-neighbour site. An SE can move over the sublattice on which it is created. A variational calculation of the GS and the GS-energy is performed for an open-ended 4 × 4 lattice with two holes with the restriction that the SE is neighbouring both holes and does not move over its sublattice. It is found that the two holes prefer a bound state in which their mutual distance is 1 or V2 (with lattice spacing 1)

Approximations to the two-hole ground state of the Hubbard-Anderson model: a numerical test

Several resonating-valence-bond-type states are being considered as an approximation of the two-hole ground state of the two-dimensional Hubbard-Anderson model. These states have been carefully constructed by Traa and Caspers with such algebraic properties, as to optimise different contributions of the Hubbard-Anderson hamiltonian. In this paper, the different contributions to their energies are calculated for lattices with sizes from 8 × 8 up to 16 × 16 and periodic boundary conditions, using a variational Monte-Carlo method. We show which state is lowest in energy and, more important, why this is so. In accordance with the optimal state from this tested set, we propose a bound state. It will be shown that this state is indeed the most stable state

The role of the Manhattan distance in antiferromagnetic ordering

The lowest state of one- and two-dimensional antiferromagnetic Heisenberg systems for a given number of "up" and "down" spins shows preference for certain regular patterns of the minority spin direction. For the one-dimensional system this pattern is an even distribution with equal distances for the minority spins, whereas in the two-dimensional systems the Manhattan distance, instead of the Euclidean distance, determines the optimal configuration