The representations of the Hubbard algebra in terms of spin-fermion operators and motion of a hole in an antiferromagnetic state

The representation of the Hubbard operators in terms of the spin$-\frac{1}{2}$ operators and the fermion operator with spin$-\frac{1}{2}$ is proposed. In the low-energy limit this representation is reduced to the representation following from the Hubbard diagramm technique. In framework of this approach motion of a hole in an antiferromagnetic state of the t-J model is considered. It is shown that the primary hole energy is strongly renormalized and the band width has an order of J rather than t. The functional integral for the strongly correlated model induced by the obtained representation is formulated. The representation of the total Hubbard algebra for states in the lower and the upper Hubbard bands is formulated in terms of the spin$-\frac{1}{2}$ and two fermion fields with spin$-\frac{1}{2}$ is formulated.Comment: 12 pp. (LATEX

Low-energy limit of the three-band model for electrons in a CuO2_{2} plane

The three-band model with the O-O direct hopping near to unit filling is considered. We present the general procedure of reduction of this model to the low-energy limit. At unit filling the three-band model in the charge-transfer limit is reduced to the Heisenberg model and we calculate the superexchange constant. For the case of the small electron doping the three-band model is reduced to the $t-J$ model and we calculate electron hopping parameters at the nearest and next neighbors. We derive the structure of corrections to the $t-J$ model and calculate their magnitude. The values of the hopping parameters for electron- and hole-doping differ approximately at 40 %.Comment: 10 pp. (LATEX

Computing the Scaling Exponents in Fluid Turbulence from First Principles: Demonstration of Multi-scaling

This manuscript is a draft of work in progress, meant for network distribution only. It will be updated to a formal preprint when the numerical calculations will be accomplished. In this draft we develop a consistent closure procedure for the calculation of the scaling exponents $\zeta_n$ of the $n$th order correlation functions in fully developed hydrodynamic turbulence, starting from first principles. The closure procedure is constructed to respect the fundamental rescaling symmetry of the Euler equation. The starting point of the procedure is an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of scaling exponents $\zeta_n$. This hierarchy was discussed in detail in a recent publication [V.S. L'vov and I. Procaccia, Phys. Rev. E, submitted, chao-dyn/9707015]. The scaling exponents in this set of equations cannot be found from power counting. In this draft we discuss in detail low order non-trivial closures of this infinite set of equations, and prove that these closures lead to the determination of the scaling exponents from solvability conditions. The equations under consideration after this closure are nonlinear integro-differential equations, reflecting the nonlinearity of the original Navier-Stokes equations. Nevertheless they have a very special structure such that the determination of the scaling exponents requires a procedure that is very similar to the solution of linear homogeneous equations, in which amplitudes are determined by fitting to the boundary conditions in the space of scales. The re-normalization scale that i necessary for any anomalous scaling appears at this point. The Holder inequalities on the scaling exponents select the renormalizaiton scale as the outer scale of turbulence $L$.Comment: 10 pages, 5 figs. to be submitted PR

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

Exact diagonalization numerical results are presented for a 32-site square cluster, with two holes propagating in an antiferromagnetic background described by the t-J model. We characterize the wave function of the lowest energy bound state found in this calculation, which has d_{x^2-y^2} symmetry. Analytical work is presented, based on a Lang-Firsov-type canonical transformation derived quasiparticle Hamiltonian, that accurately agrees with numerically determined values for the electron momentum distribution function and the pair correlation function. We interpret this agreement as strong support for the validity of this description of the hole quasiparticles.Comment: 3 pages, REVTeX, to appear in the proceedings of the Fifth International Conference on Spectroscopies in Novel Superconductors, September 14-18, 1997, Cape Cod, Massachusett

Holes in the t-J_z model: a thorough study

The t-J_z model is the strongly anisotropic limit of the t-J model which captures some general properties of the doped antiferromagnets (AF). The absence of spin fluctuations simplifies the analytical treatment of hole motion in an AF background and allows us to calculate the single- and two-hole spectra with high accuracy using regular diagram technique combined with real-space approach. At the same time, numerical studies of this model via exact diagonalization (ED) on small clusters show negligible finite size effects for a number of quantities, thus allowing a direct comparison between analytical and numerical results. Both approaches demonstrate that the holes have tendency to pair in the p- and d-wave channels at realistic values of t/J. The interactions leading to pairing and effects selecting p and d waves are thoroughly investigated. The role of transverse spin fluctuations is considered using perturbation theory. Based on the results of the present study, we discuss the pairing problem in the realistic t-J-like model. Possible implications for preformed pairs formation and phase separation are drawn.Comment: 21 pages, 15 figure

Reversality of optical interactions in noncentrosymmetric media

The interaction of an electromagnetic wave with a noncentrosymmetric crystal is not necessarily time reversible, and the departure from reversality may be seen in nonlocal (wave-vector linear) phenomena. However, relativistic symmetry with respect to simultaneous time and space inversion is always preserved in optics

Possible propagation of the Zhang-Rice singlet as a probable Cooper channel in the CuO2CuO_2 planes

The issue of how superconductivity originate in the $CuO_2$ planes believed to be crucial to understanding the high $T_c$ superconducting cuprates is still an going debate. In the wake of recent experimental observations of the the Zhang-Rice singlet (ZRS), its formation and propagation need to be revisited especially by using a simple approach almost at a phenomenological level. Within a highly simplified correlated variational approach (HSCVA) in this paper, a new formation of the ZRS as constituting the ground state of a single-band t-J model of the $CuO_2$ planes is developed. This formation is then used to demonstrate how the ZRS can be propagated as a probable Cooper channel in the $CuO_2$ planes.Comment: 10 page

Dynamics of Passive-Scalar Turbulence

We present the first study of the dynamic scaling or multiscaling of passive-scalar and passive-vector turbulence. For the Kraichnan version of passive-scalar and passive-vector turbulence we show analytically, in both Eulerian and quasi-Lagrangian frameworks, that simple dynamic scaling is obtained but with different dynamic exponents. By developing the multifractal model we show that dynamic multiscaling occurs in passive-scalar turbulence only if the advecting velocity field is itself multifractal. We substantiate our results by detailed numerical simulations in shell models of passive-scalar advection.Comment: published versio