Electronic Correlations within Fermionic Lattice Models

We investigate two-site electronic correlations within generalized Hubbard model, which incorporates the conventional Hubbard model (parameters: $t$ (hopping between nearest neighbours), $U$ (Coulomb repulsion (attraction)) supplemented by the intersite Coulomb interactions (parameters: $J^{(1)}$(parallel spins), $J^{(2)}$ (antiparellel spins)) and the hopping of the intrasite Cooper pairs (parameter: $V$). As a first step we find the eigenvalues $E_{\alpha}$ and eigenvectors $|E_{\alpha}>$ of the dimer and we represent each partial Hamiltonian $E_{\alpha} |E_{\alpha} > < E_{\alpha} |$ ($\alpha =1,2,..,16$) in the second quantization with the use of the Hubbard and spin operators. Each dimer energy level possesses its own Hamiltonian describing different two-site interactions which can be active only in the case when the level will be occupied by the electrons. A typical feature is the appearence of two generalized $t-J$ interactions ascribed to two different energy levels which do not vanish even for $$ and their coupling constants are equal to $\pm t$ in this case. The competition between ferromagnetism, antiferromagnetism and superconductivity (intrasite and intersite pairings) is also a typical feature of the model because it persists in the case $U=J^{(1)}=J^{(2)}=V=0$ and $t\neq 0$. The same types of the electronic, competitive interactions are scattered between different energy levels and therefore their thermodynamical activities are dependent on the occupation of these levels. It qualitatively explains the origin of the phase diagram of the model. We consider also a real lattice as a set of interacting dimers to show that the competition between magnetism and superconductivity seems to be universal for fermonic lattice models.Comment: 12 page

Hubbard Hamiltonian in the dimer representation. Large U limit

We formulate the Hubbard model for the simple cubic lattice in the representation of interacting dimers applying the exact solution of the dimer problem. By eliminating from the considerations unoccupied dimer energy levels in the large U limit (it is the only assumption) we analytically derive the Hubbard Hamiltonian for the dimer (analogous to the well-known t-J model), as well as, the Hubbard Hamiltonian for the crystal as a whole by means of the projection technique. Using this approach we can better visualize the complexity of the model, so deeply hidden in its original form. The resulting Hamiltonian is a mixture of many multiple ferromagnetic, antiferromagnetic and more exotic interactions competing one with another. The interplay between different competitive interactions has a decisive influence on the resulting thermodynamic properties of the model, depending on temperature, model parameters and assumed average number of electrons per lattice site. A simplified form of the derived Hamiltonian can be obtained using additionally Taylor expansion with respect to $x=\frac{t}{U}$ (t-hopping integral between nearest neighbours, U-Coulomb repulsion). As an example, we present the expansion including all terms proportional to t and to $\frac{t^2}U$ and we reproduce the exact form of the Hubbard Hamiltonian in the limit $U\to \infty$. The nonperturbative approach, presented in this paper, can, in principle, be applied to clusters of any size, as well as, to another types of model Hamiltonians.Comment: 26 pages, 1 figure, LaTeX; added reference

Extended Hubbard model in the dimer representation.[Cz.] 1 Dimer Hamiltonian in the large U limit

We consider the extended Hubbard model for the single cubic lattice and rewrite it in the form of interacting dimers, using the exact solution of the dimer problem. We analytically derive the second quantization form of the dimer Hamiltoni an eliminating from the considerations unoccupieddimer energy levels in the large U limit (it is the only assumption ). The resulting dimer Hamiltonian written with the use of the Hubbard operators and spin operators contains three terms, visualizing explicitly competing magnetic interactions (ferromagnetic, antiferromagnetic) as a generalization of the t -J model. The presented, nonperturbative method, can in principle be applied to the cluster of any size (e.g. one central atom and z its nearest neighbours). The use of the projection technique can further be applied in the case of a crystal to obtain the second quantization form of the extended Hubbard model for the sclattice in the large U limit

Extended Hubbard model in the dimer representation.[Cz.] 2 Dimer Hamiltonian in the large U limit

Using the exact decomposition of the sclattice into a set of interacting dimers (each dimer is described by the extended Hubbard Hamiltonian) and exact solution of the dimer problem (preceding paper) we exactly find the form of the extended Hubbard model in the case of a crystal in the large U limit. We apply a new, nonperturbative approach based on the exact projection procedure onto a dimer subspace occupied by electrons in this limit (it is the only assumption). The resulting Hamiltonian is very complicated and contains a variety of multiple magnetic and nonmagnetic interactions deeply hidden in its original form (site representation). We also present a simplified version of the model to better visualize a mixture of different interactions resulting from this approach

Chemical potential as a detector of phase transitions in solids

We show that the chemical potential exhibits small but distinct kinks at all critical temperatures as the evidence for phase transitions in the electronic system, structural phase transitions included. In the case of, at least, two kinds of interacting electrons average occupation numbers exhibit the same behavior

A Pixel Vertex Tracker for the TESLA Detector

In order to fully exploit the physics potential of a e+e- linear collider, such as TESLA, a Vertex Tracker providing high resolution track reconstruction is required. Hybrid Silicon pixel sensors are an attractive sensor technology option due to their read-out speed and radiation hardness, favoured in the high rate TESLA environment, but have been so far limited by the achievable single point space resolution. A novel layout of pixel detectors with interleaved cells to improve their spatial resolution is introduced and the results of the characterisation of a first set of test structures are discussed. In this note, a conceptual design of the TESLA Vertex Tracker, based on hybrid pixel sensors is presentedComment: 20 pages, 11 figure

High resolution pixel detectors for e+e- linear colliders

The physics goals at the future e+e- linear collider require high performance vertexing and impact parameter resolution. Two possible technologies for the vertex detector of an experimental apparatus are outlined in the paper: an evolution of the Hybrid Pixel Sensors already used in high energy physics experiments and a new detector concept based on the monolithic CMOS sensors.Comment: 8 pages, to appear on the Proceedings of the International Workshop on Linear Colliders LCWS99, Sitges (Spain), April 28 - May 5, 199

High Resolution Hybrid Pixel Sensors for the e+e- TESLA Linear Collider Vertex Tracker

In order to fully exploit the physics potential of a future high energy e+e- linear collider, a Vertex Tracker, providing high resolution track reconstruction, is required. Hybrid Silicon pixel sensors are an attractive option, for the sensor technology, due to their read-out speed and radiation hardness, favoured in the high rate environment of the TESLA e+e- linear collider design but have been so far limited by the achievable single point space resolution. In this paper, a conceptual design of the TESLA Vertex Tracker, based on a novel layout of hybrid pixel sensors with interleaved cells to improve their spatial resolution, is presented.Comment: 12 pages, 5 figures, to appear in the Proceedings of the Vertex99 Workshop, Texel (The Netherlands), June 199