The representations of the degenerate affine Hecke algebra in which the analogues of the Dunkl operators are given by finite-difference operators are introduced. The non-selfadjoint lattice analogues of the spin Calogero-Sutherland hamiltonians are analysed by Bethe-Ansatz. The sl(m)-Yangian representations arising from the finite-difference representations of the degenerate affine Hecke algebr...

We present a mapping of elementary fermion operators onto a quadratic form of composite fermionic and bosonic cluster operators. The mapping is an exact isomorphism as long as the physical constraint of one composite particle per cluster is satisfied. This condition is treated on average in a composite particle mean-field approach, which consists of an ansatz that decouples the composite fermio...

Using a two-channel Anderson model, we develop a theory of composite pairing in the 115 family of heavy fermion superconductors that incorporates the effects of f -electron valence fluctuations. Our calculations introduce “symplectic Hubbard operators”: an extension of the slave boson Hubbard operators that preserves both spin rotation and time-reversal symmetry in a large N expansion, permitti...

We develop a general scheme for the use of Fermi operators within the framework of integrable systems. This enables us to read off a fermionic Hamiltonian from a given solution of the YangBaxter equation and to express the corresponding L-matrix and the generators of symmetries in terms of Fermi operators. We illustrate our approach through a number of examples. Our main example is the algebrai...

Ground state energies and on-site density-density correlations are calculated for the 1-D Hubbard model using a linear combination of the Hubbard projection operators. The mean-eld coeecients in the resulting linearized Equations of Motion (EOM) depend on both one-particle static expectation values as well as static two-particle correlations. To test the model, the one particle expectation valu...

A new two-pole approximation in the Hubbard model. Two-pole approaches in the Hubbard model [1] and the Hubbard bands conception (being the consequence of a two-pole approximation) have been useful for understanding of the peculiarities of electric and magnetic properties of narrow-band materials [1]-[13]. However within the framework of two-pole approaches there are series of issues, in partic...

Recent results, extending the Schmidt decomposition theorem to wavefunctions of pairs of identical particles, are reviewed. They are used to give a definition of reduced density operators in the case of two identical particles. Next, a method is discussed to calculate time averaged entanglement. It is applied to a pair of identical electrons in an otherwise empty band of the Hubbard model, and ...

The one-dimensional Hubbard model is integrable in the sense that it has an infinite family of conserved currents. We explicitly construct a ladder operator which can be used to iteratively generate all of the conserved current operators. This construction is different from that used for Lorentz invariant systems such as the Heisenberg model. The Hubbard model is not Lorentz invariant, due to t...

Recent results, extending the Schmidt decomposition theorem to wavefunctions of identical particles, are reviewed. They are used to give a definition of reduced density operators in the case of two identical particles. Next, a method is discussed to calculate time averaged entanglement. It is applied to a pair of identical electrons in an otherwise empty band of the Hubbard model, and to a pair...