Completeness of singlet pair states for quantum spin systems

It is shown that for an arbitrary subdivision of an antiferromagnetic spin- lattice into two subsystems every singlet state can be expressed as a linear combination of single pair states (SPS). These SPS states are products of singlet states for a pair of representatives of either subsystem

Renormalization techniques for quantum spin systems. Ground-state energies

Projection of the Hamiltonian of an antiferromagnetic lattice of spins , without external fields, onto a subspace of the total spinor space gives an approximation for the lowest eigenvalue of this Hamiltonian. Repeated projection results in a series expansion for this approximation. In each projection the form of the Hamiltonian is conserved. The formal structure of this projection technique shows a strong analogy with the Wilson theory or renormalization-group theory of phase transitions. Numerical results are given for linear chains and triangular lattice

On the existence of a gap in the energy spectrum of quantum systems

A theorem on the existence of a gap in the energy spectrum of quantum systems, the exact ground state of which is known explicitly, is proved. The theorem is applied to a three-dimensional Heisenberg spin-1/2 ferromagnet, with anisotropic nearest-neighbour interactions, and to an alternating Heisenberg antiferromagnet, with nearest- and next-nearest-neighbour interactions

Level crossing and the space of operators commuting with the Hamiltonian

The space of n-dimensional hermitean matrices that commute with a given hermitean matrix A + hB, h being a real parameter, is discussed. In particular a basis in this space is constructed consisting of polynomials in h of the lowest possible total degree. The sum of the degrees of the elements of this minimal basis equals 1/2n((n-1) - q , q being the number of linearly independent linear relations between the symmetrized products of A and B of order 0,…,n − 1. These linear relations determine the values of h for which crossing occurs, the total number of crossings for each value, and in some cases the order of the different crossings. A discussion of the noncrossing rule concludes this paper.\u

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

Rotational ordering and symmetry breaking in the triangular antiferromagnetic Heisenberg lattice

Finite system calculations suggest a rotational ordering in the ground state of the triangular antiferromagnetic Heisenberg lattice. This rotational ordering may result in a rotational symmetry breaking for quantum-spin systems, which does not show a net sublattice magnetization

Some exact excited states in a linear antiferromagnetic spin system

Exact expressions are derived for some excited states in a linear quantum spin system for which the exact ground state has been studied in the last decade

Elementary excitations in antiferromagnetic Heisenberg systems

The structure of the (eigen)states of antiferromagnetic Heisenberg systems is discussed. These systems are shown to be equivalent to classical systems of coupled harmonic oscillators. Most attention will be paid to the first excited state. This state is supposed to be a triplet. An approximation method, which is a generalization of a method, used to describe the ground state of Heisenberg systems, will be used to describe elementary excitations. The working of the method is demonstrated by some small-system calculations

Exact spectrum for n electrons in the single band Hubbard model

The energy spectrum and the correlation functions for n electrons in the one-dimensional single band Hubbard model with periodic boundary conditions are calculated exactly. For that purpose the Hamiltonian is transformed into a set of Hamiltonians, corresponding to systems of spinless fermions.\ud Our results include the results of Mei and Chen, presented in a recent paper

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