11,152 research outputs found

    Exact Solution of a One-Dimensional Multicomponent Lattice Gas with Hyperbolic Interaction

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    We present the exact solution to a one-dimensional multicomponent quantum lattice model interacting by an exchange operator which falls off as the inverse-sinh-square of the distance. This interaction contains a variable range as a parameter, and can thus interpolate between the known solutions for the nearest-neighbor chain, and the inverse-square chain. The energy, susceptibility, charge stiffness and the dispersion relations for low-lying excitations are explicitly calculated for the absolute ground state, as a function of both the range of the interaction and the number of species of fermions.Comment: 13 REVTeX pages + 5 uuencoded figures, UoU-003059

    Algorithms to solve the Sutherland model

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    We give a self-contained presentation and comparison of two different algorithms to explicitly solve quantum many body models of indistinguishable particles moving on a circle and interacting with two-body potentials of 1/sin21/\sin^2-type. The first algorithm is due to Sutherland and well-known; the second one is a limiting case of a novel algorithm to solve the elliptic generalization of the Sutherland model. These two algorithms are different in several details. We show that they are equivalent, i.e., they yield the same solution and are equally simple.Comment: 15 pages, LaTe

    Spectral flow in the supersymmetric tt-JJ model with a 1/r21/r^2 interaction

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    The spectral flow in the supersymmetric {\it t-J} model with 1/r21/r^2 interaction is studied by analyzing the exact spectrum with twisted boundary conditions. The spectral flows for the charge and spin sectors are shown to nicely fit in with the motif picture in the asymptotic Bethe ansatz. Although fractional exclusion statistics for the spin sector clearly shows up in the period of the spectral flow at half filling, such a property is generally hidden once any number of holes are doped, because the commensurability condition in the motif is not met in the metallic phase.Comment: 8 pages, revtex, Phys. Rev. B54 (1996) August 15, in pres

    Dyson's Brownian Motion and Universal Dynamics of Quantum Systems

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    We establish a correspondence between the evolution of the distribution of eigenvalues of a N×NN\times N matrix subject to a random Gaussian perturbing matrix, and a Fokker-Planck equation postulated by Dyson. Within this model, we prove the equivalence conjectured by Altshuler et al between the space-time correlations of the Sutherland-Calogero-Moser system in the thermodynamic limit and a set of two-variable correlations for disordered quantum systems calculated by them. Multiple variable correlation functions are, however, shown to be inequivalent for the two cases.Comment: 10 pages, revte

    Partially Solvable Anisotropic t-J Model with Long-Range Interactions

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    A new anisotropic t-J model in one dimension is proposed which has long-range hopping and exchange. This t-J model is only partially solvable in contrast to known integrable models with long-range interaction. In the high-density limit the model reduces to the XXZ chain with the long-range exchange. Some exact eigenfunctions are shown to be of Jastrow-type if certain conditions for an anisotropy parameter are satisfied. The ground state as well as the excitation spectrum for various cases of the anisotropy parameter and filling are derived numerically. It is found that the Jastrow-type wave function is an excellent trial function for any value of the anisotropy parameter.Comment: 10 pages, 3 Postscript figure

    Universal Level dynamics of Complex Systems

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    . We study the evolution of the distribution of eigenvalues of a N×NN\times N matrix subject to a random perturbation drawn from (i) a generalized Gaussian ensemble (ii) a non-Gaussian ensemble with a measure variable under the change of basis. It turns out that, in the case (i), a redefinition of the parameter governing the evolution leads to a Fokker-Planck equation similar to the one obtained when the perturbation is taken from a standard Gaussian ensemble (with invariant measure). This equivalence can therefore help us to obtain the correlations for various physically-significant cases modeled by generalized Gaussian ensembles by using the already known correlations for standard Gaussian ensembles. For large NN-values, our results for both cases (i) and (ii) are similar to those obtained for Wigner-Dyson gas as well as for the perturbation taken from a standard Gaussian ensemble. This seems to suggest the independence of evolution, in thermodynamic limit, from the nature of perturbation involved as well as the initial conditions and therefore universality of dynamics of the eigenvalues of complex systems.Comment: 11 Pages, Latex Fil

    Thermodynamics of an one-dimensional ideal gas with fractional exclusion statistics

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    We show that the particles in the Calogero-Sutherland Model obey fractional exclusion statistics as defined by Haldane. We construct anyon number densities and derive the energy distribution function. We show that the partition function factorizes in the form characteristic of an ideal gas. The virial expansion is exactly computable and interestingly it is only the second virial coefficient that encodes the statistics information.Comment: 10pp, REVTE

    GAPS IN THE HEISENBERG-ISING MODEL

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    We report on the closing of gaps in the ground state of the critical Heisenberg-Ising chain at momentum π\pi. For half-filling, the gap closes at special values of the anisotropy Δ=cos(π/Q)\Delta= \cos(\pi/Q), QQ integer. We explain this behavior with the help of the Bethe Ansatz and show that the gap scales as a power of the system size with variable exponent depending on Δ\Delta. We use a finite-size analysis to calculate this exponent in the critical region, supplemented by perturbation theory at Δ0\Delta\sim 0. For rational 1/r1/r fillings, the gap is shown to be closed for {\em all} values of Δ\Delta and the corresponding perturbation expansion in Δ\Delta shows a remarkable cancellation of various diagrams.Comment: 12 RevTeX pages + 4 figures upon reques
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