A self-consistent, conserving theory of the attractive Hubbard model in two dimensions

We have investigated the attractive Hubbard model in the low density limit for the 2D square lattice using the ladder approximation for the vertex function in a self-consistent, conserving formulation. In the parameter region where the on-site attraction is of the order of the bandwidth, we found no evidence of a pseudo gap. Further, we have observed that the suppression of the Fermi surface known to destroy superconductivity in one and two dimensions, when these systems are treated using a non self-consistent theory (Schmitt-Rink, et al., Phys. Rev. Lett. 63, 445 (1989)), does not occur when pair-pair interactions are included. However, we do find a quasiparticle lifetime that varies linearly with temperature, similar to many experiments. Thus, although this system has a Fermi surface, it shows non Fermi liquid type behaviour over a wide temperature range. We stress that our work uses thermal Green's functions along the real time axis, and thus allows for a more accurate determination of the dynamical properties of a model than theories that require extrapolations from the imaginary frequency axis.Comment: 13 pages, including 14 figure

Incorporating the Hayflick Limit into a model of Telomere Dynamics

A model of telomere dynamics is proposed and examined. Our model, which extends a previously introduced two-compartment model that incorporates stem cells as progenitors of new cells, imposes the Hayflick Limit, the maximum number of cell divisions that are possible. This new model leads to cell populations for which the average telomere length is not necessarily a monotonically decreasing function of time, in contrast to previously published models. We provide a phase diagram indicating where such results would be expected. In addition, qualitatively different results are obtained for the evolution of the total cell population. Last, in comparison to available leukocyte baboon data, this new model is shown to provide a better fit to biological data

Magnetic susceptibility of the body-centred orthorhombic La2_2CuO4_4 system

A model Hamiltonian representing the Cu spins in La$_2$CuO$_4$ in its low-temperature body-centred orthorhombic phase, that includes both spin-orbit generated Dzyaloshinskii-Moriya interactions and interplanar exchange, is examined within the RPA utilizing a Tyablikov decoupling of various high-order Green's functions. The magnetic susceptibility is evaluated as a function of temperature and the parameters quantifying these interactions, and compared to recently obtained experimental data of Lavrov, Ando and collaborators. An effective Hamiltonian corresponding to a simple tetragonal structure is shown to reproduce both the magnon spectra and the susceptibility of the more complicated body-centred orthorhombic model.Comment: 32 pages, 17 figure

Pairing Fluctuations in The Attractive Hubbard Model in the Atomic Limit

BCS theory accounts for the pairing instability in the weak coupling limit, but fails to describe pairing fluctuations above $T_c$. One possibility for describing these fluctuations in the dilute limit is the T-matrix approximation. We critically examine various degrees of self-consistency in the T-matrix formalism, along with a non-diagrammatic two-particle self-consistent (TPSC) formulation, in the strong coupling regime, where an exact solution is readily available. We find that one particular degree of self-consistency is quite accurate, particularly at low temperature as evidenced by examining both static and dynamic properties.Comment: 5 pages, 3 figure

A Comprehensive Dynamical Study of Nucleation and Growth in a One--Dimensional Shear Martensitic Transition

We have constructed a complete hydrodynamic theory of nucleation and growth in a one--dimensional version of an elastic shear martensitic transformation with open boundary conditions where we have accounted for interfacial energies with strain--gradient contributions. We have studied the critical martensitic nuclei for this problem: Interestingly, the bulk critical nuclei are {\em twinned} structures, although we have determined that the dominant route for the formation of martensite is through {\em surface nucleation}. We have analytically solved for the surface nuclei and evaluated exact nucleation rates showing the strong preference for surface nucleation. We have also examined the growth of martensite: There are two possible martensitic growth fronts, {\em viz}., dynamical twinning and so-called two--kink solutions. These transformation fronts are separated by a {\em dynamical} phase transition. We analytically derive this phase diagram and determine expressions for the speeds of the martensitic growth fronts.Comment: 17 Postscript figures, to appear in Met. Trans

Exact diagonalization analysis of the Anderson-Hubbard model and comparison to real-space self-consistent Hartree-Fock solutions

We have obtained the exact ground state wave functions of the Anderson-Hubbard model for different electron fillings on a 4x4 lattice with periodic boundary conditions - for 1/2 filling such ground states have roughly 166 million states. When compared to the uncorrelated ground states (Hubbard interaction set to zero) we have found strong evidence of the very effective screening of the charge homogeneities due to the Hubbard interaction. We have successfully modelled these local charge densities using a non-interacting model with a static screening of the impurity potentials. In addition, we have compared such wave functions to self-consistent real-space unrestricted Hartree-Fock solutions and have found that these approximate ground state wave functions are remarkably successful at reproducing the local charge densities, and may indicate the role of dipolar backflow in producing a novel metallic state in two dimensions

Increasing Superconducting Tc's by a Factor of 1000 with StripeLike Hopping Anisotropies

We have studied the enhancement of the superconducting transition temperature, Tc, in a t-J-U model of electrons moving on a square lattice in which anisotropic electronic hopping is introduced. The inclusion of such hopping mimics, in a approximate fashion, a potentially important characteristic of materials possessing stripelike charge and spin correlations. For this model we have calculated Tc for singlet pairing using the non self-consistent Thouless criterion, and find a dramatic enhancement of Tc induced by hopping anisotropies. Further, the maximum increase in Tc is obtained when the system is pushed towards the extreme anisotropy limit, that is, when the hopping of electrons is confined to occur in 1+0^+ dimensions. We demonstrate that in this limit the increase in Tc, with respect to the isotropic system, can be of the order of 1000. We have also determined that in the extreme anisotropy limit the superconducting gap is an equal mixture of s and d pairing symmetries (two choices of such a combination being s + d and s + id) owing to the reduced (square to rectangular) symmetry of the system in the presence of hopping anisotropies. Thus, the presence of d-wave superconducting features in materials whose symmetry is very different from that of a two-dimensional square lattice, with the anisotropy produced by the appearance of stripes, is not unexpected.Comment: 8 pages (Revtex), 4 eps figure

Examining the metal-to-insulator transitions in Li1+xTi2-xO4 and LiAlyTi2-yO4 with a Quantum Site Percolation model

We have studied the composition-induced metal-to-insulator transitions of cation substituted Lithium Titanate, in the forms Li1+xTi2-xO4 and LiAlyTi2-yO4, utilising a quantum site percolation model, and we argue that such a model provides a very reliable representation of the noninteracting electrons in this material if strong correlations are ignored. We then determine whether or not such a model of 3d electrons moving on the Ti (corner-sharing tetrahedral) sublattice describes the observed metal-to-insulator transitions, with the critical concentration defined by the matching of the mobility edge and the chemical potential. Our analysis leads to quantitative predictions that are in disagreement with those measured experimentally. For example, experimentally for the LiAlyTi2-yO4 compound an Al concentration of y_c approximately 0.33 produces a metal-to-insulator transition, whereas our analysis of a quantum site percolation model predicts y_c approximately 0.83. One hypothesis that is consistent with these results is that since strong correlations are ignored in our quantum site percolation model, which includes the effects of configurational disorder only, such strong electronic correlations are both present and important.Comment: 5 pages, 4 figure

Theory of Coexisting Transverse Spin Freezing and Long-Ranged Antiferromagnetic Order in Lightly Doped La_{2-x}Sr_x CuO_4

We provide an explanation of the spin-freezing transition recently observed by Chou et al. (Phys. Rev. Lett. 71, 2323 (1993)) in La_{2-x}Sr_x CuO_4 for x <= 0.02. We propose that topological excitations of the 2D Heisenberg quantum antiferromagnet having non-coplanar transverse components have a pair-interaction energy that qualitatively and quantitatively agrees with the observed values of spin-freezing temperature as a function of doping.Comment: 18 pages, figures available upon request, revtex, 500

A comprehensive numerical and analytical study of two holes doped into the 2D t-J model

We report on a detailed examination of numerical results and analytical calculations devoted to a study of two holes doped into a two-dimensional, square lattice described by the t-J model. Our exact diagonalization numerical results represent the first solution of the exact ground state of 2 holes in a 32-site lattice. Using this wave function, we have calculated several important correlation functions, notably the electron momentum distribution function and the hole-hole spatial correlation function. Further, by studying similar quantities on smaller lattices, we have managed to perform a finite-size scaling analysis. We have augmented this work by endeavouring to compare these results to the predictions of analytical work for two holes moving in an infinite lattice. This analysis relies on the canonical transformation approach formulated recently for the t-J model. From this comparison we find excellent correspondence between our numerical data and our analytical calculations. We believe that this agreement is an important step helping to justify the quasiparticle Hamiltonian, and in particular, the quasiparticle interactions, that result from the canonical transformation approach. Also, the analytical work allows us to critique the finite-size scaling ansatzes used in our analysis of the numerical data. One important feature that we can infer from this successful comparison involves the role of higher harmonics in the two-particle, d-wave symmetry bound state -- the conventional (\cos(k_x) - \cos(k_y)) term is only one of many important contributions to the d-wave symmetry pair wave function.Comment: RevTeX, 25 pages, 15 figures included. One major typo is correcte