11,152 research outputs found

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

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

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
$1/\sin^2$-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 $t$-$J$ model with a $1/r^2$ interaction

The spectral flow in the supersymmetric {\it t-J} model with $1/r^2$
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

We establish a correspondence between the evolution of the distribution of
eigenvalues of a $N\times N$ 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

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

. We study the evolution of the distribution of eigenvalues of a $N\times N$
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 $N$-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

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

We report on the closing of gaps in the ground state of the critical
Heisenberg-Ising chain at momentum $\pi$. For half-filling, the gap closes at
special values of the anisotropy $\Delta= \cos(\pi/Q)$, $Q$ 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 $\Delta$. We use
a finite-size analysis to calculate this exponent in the critical region,
supplemented by perturbation theory at $\Delta\sim 0$. For rational $1/r$
fillings, the gap is shown to be closed for {\em all} values of $\Delta$ and
the corresponding perturbation expansion in $\Delta$ shows a remarkable
cancellation of various diagrams.Comment: 12 RevTeX pages + 4 figures upon reques

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