10,506 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
Solution of Some Integrable One-Dimensional Quantum Systems
In this paper, we investigate a family of one-dimensional multi-component
quantum many-body systems. The interaction is an exchange interaction based on
the familiar family of integrable systems which includes the inverse square
potential. We show these systems to be integrable, and exploit this
integrability to completely determine the spectrum including degeneracy, and
thus the thermodynamics. The periodic inverse square case is worked out
explicitly. Next, we show that in the limit of strong interaction the "spin"
degrees of freedom decouple. Taking this limit for our example, we obtain a
complete solution to a lattice system introduced recently by Shastry, and
Haldane; our solution reproduces the numerical results. Finally, we emphasize
the simple explanation for the high multiplicities found in this model
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
Universal Level dynamics of Complex Systems
. We study the evolution of the distribution of eigenvalues of a
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 -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
Density Correlation Functions in Calogero Sutherland Models
Using arguments from two dimensional Yang-Mills theory and the collective
coordinate formulation of the Calogero-Sutherland model, we conjecture the
dynamical density correlation function for coupling and , where is
an integer. We present overwhelming evidence that the conjecture is indeed
correct.Comment: 12 pages phyzzx, CERN-TH/94.7243 One reference change
Crossover from Fermi Liquid to Non-Fermi Liquid Behavior in a Solvable One-Dimensional Model
We consider a quantum moany-body problem in one-dimension described by a
Jastrow type, characterized by an exponent and a parameter .
We show that with increasing , the Fermi Liquid state (
crosses over to non-Fermi liquid states, characterized by effective
"temperature".Comment: 8pp. late
Solutions to the Multi-Component 1/R Hubbard Model
In this work we introduce one dimensional multi-component Hubbard model of
1/r hopping and U on-site energy. The wavefunctions, the spectrum and the
thermodynamics are studied for this model in the strong interaction limit
. In this limit, the system is a special example of Luttinger
liquids, exhibiting spin-charge separation in the full Hilbert space.
Speculations on the physical properties of the model at finite on-site energy
are also discussed.Comment: 9 pages, revtex, Princeton-May1
Supersymmetry, Shape Invariance and Solvability of and Calogero-Sutherland Model
Using the ideas of supersymmetry and shape invariance we re-derive the
spectrum of the and Calogero-Sutherland model. We briefly
discuss as to how to obtain the corresponding eigenfunctions. We also discuss
the difficulties involved in extending this approach to the trigonometric
models.Comment: 15 pages, REVTeX,No figure
Exact Solution of Heisenberg-liquid models with long-range coupling
We present the exact solution of two Heisenberg-liquid models of particles
with arbitrary spin interacting via a hyperbolic long-range potential. In
one model the spin-spin coupling has the simple antiferromagnetic Heisenberg
exchange form, while for the other model the interaction is of the
ferromagnetic Babujian-Takhatajan type. It is found that the Bethe ansatz
equations of these models have a similar structure to that of the
Babujian-Takhatajan spin chain. We also conjecture the integrability of a third
new spin-lattice model with long-range interaction.Comment: 7pages 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 . For half-filling, the gap closes at
special values of the anisotropy , 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 . We use
a finite-size analysis to calculate this exponent in the critical region,
supplemented by perturbation theory at . For rational
fillings, the gap is shown to be closed for {\em all} values of and
the corresponding perturbation expansion in shows a remarkable
cancellation of various diagrams.Comment: 12 RevTeX pages + 4 figures upon reques
- …