10,109 research outputs found
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
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
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
A Mean Field Analysis of One Dimensional Quantum Liquid with Long Range Interaction
Bi-local mean field theory is applied to one dimensional quantum liquid with
long range interaction, which has exact ground state wave function. We
obtain a mean field solution and an effective action which expresses a long
range dynamics. Based on them the ground state energy and correlation functions
are computed. The ground state energy agrees fairly well with the exact value
and exponents have weaker coupling constant dependence than that of partly
known exact value.Comment: EPHOU-93-002, 10 pages (LaTeX), 3 figures available upon request as
hard cop
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
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
Spectrum and Thermodynamics of the one-dimensional supersymmetric t-J model with exchange and hopping
We derive the spectrum and the thermodynamics of the one-dimensional
supersymmetric t-J model with long range hopping and spin exchange using a set
of maximal-spin eigenstates. This spectrum confirms the recent conjecture that
the asymptotic Bethe-ansatz spectrum is exact. By empirical determining the
spinon degeneracies of each state, we are able to explicitly construct the free
energy.Comment: 13 pages, Latex, (published in PRB46, 6639 (1992)
Transport Properties of a One-Dimensional Two-Component Quantum Liquid with Hyperbolic Interactions
We present an investigation of the sinh-cosh (SC) interaction model with
twisted boundary conditions. We argue that, when unlike particles repel, the SC
model may be usefully viewed as a Heisenberg-Ising fluid with moving
Heisenberg-Ising spins. We derive the Luttinger liquid relation for the
stiffness and the susceptibility, both from conformal arguments, and directly
from the integral equations. Finally, we investigate the opening and closing of
the ground state gaps for both SC and Heisenberg-Ising models, as the
interaction strength is varied.Comment: 10 REVTeX pages + 4 uuencoded figures, UoU-002029
Nonlocal effects in the shot noise of diffusive superconductor - normal-metal systems
A cross-shaped diffusive system with two superconducting and two normal
electrodes is considered. A voltage is applied between the normal
leads. Even in the absence of average current through the superconducting
electrodes their presence increases the shot noise at the normal electrodes and
doubles it in the case of a strong coupling to the superconductors. The
nonequilibrium noise at the superconducting electrodes remains finite even in
the case of a vanishingly small transport current due to the absence of energy
transfer into the superconductors. This noise is suppressed by
electron-electron scattering at sufficiently high voltages.Comment: 4 pages, RevTeX, 2 eps figure
Connection between Calogero-Marchioro-Wolfes type few-body models and free oscillators
We establish the exact correspondence of the Calogero-Marchioro-Wolfes model
and several of its generalizations with free oscillators. This connection
yields the eigenstates and leads to a proof of the quantum integrability. The
usefulness of our method for finding new solvable models is then demonstrated
by an example.Comment: 10 pages, REVTeX, Minor correction
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