53 research outputs found
Electron Addition Spectrum in the Supersymmetric t-J Model with Inverse-Square Interaction
The electron addition spectrum A^+(k,omega) is obtained analytically for the
one-dimensional (1D) supersymmetric t-J model with 1/r^2 interaction. The
result is obtained first for a small-sized system and its validity is checked
against the numerical calculation. Then the general expression is found which
is valid for arbitrary size of the system. The thermodynamic limit of
A^+(k,omega) has a simple analytic form with contributions from one spinon, one
holon and one antiholon all of which obey fractional statistics. The upper edge
of A^+(k,omega) in the (k,omega) plane includes a delta-function peak which
reduces to that of the single-electron band in the low-density limit.Comment: 5 pages, 1 figure, accepted for publication in Phys. Rev. Let
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
Derivation of Green's Function of Spin Calogero-Sutherland Model by Uglov's Method
Hole propagator of spin 1/2 Calogero-Sutherland model is derived using
Uglov's method, which maps the exact eigenfunctions of the model, called
Yangian Gelfand-Zetlin basis, to a limit of Macdonald polynomials (gl_2-Jack
polynomials). To apply this mapping method to the calculation of 1-particle
Green's function, we confirm that the sum of the field annihilation operator on
Yangian Gelfand-Zetlin basis is transformed to the field annihilation operator
on gl_2-Jack polynomials by the mapping. The resultant expression for hole
propagator for finite-size system is written in terms of renormalized momenta
and spin of quasi-holes and the expression in the thermodynamic limit coincides
with the earlier result derived by another method. We also discuss the
singularity of the spectral function for a specific coupling parameter where
the hole propagator of spin Calogero-Sutherland model becomes equivalent to
dynamical colour correlation function of SU(3) Haldane-Shastry model.Comment: 36 pages, 8 figure
Coordinate Representation of the One-Spinon One-Holon Wavefunction and Spinon-Holon Interaction
By deriving and studying the coordinate representation for the one-spinon
one-holon wavefunction we show that spinons and holons in the supersymmetric model with interaction attract each other. The interaction causes
a probability enhancement in the one-spinon one-holon wavefunction at short
separation between the particles. We express the hole spectral function for a
finite lattice in terms of the probability enhancement, given by the one-spinon
one-holon wavefunction at zero separation. In the thermodynamic limit, the
spinon-holon attraction turns into the square-root divergence in the hole
spectral function.Comment: 20 pages, 3 .eps figure
Elementary Excitations and Dynamical Correlation Functions of the Calogero-Sutherland Model with Internal Symmetry
We consider the physical properties of elementary excitations of the
Calogero-Sutherland (CS) model with SU(K) internal symmetry. From the results
on the thermodynamics of this model, we obtain the charge, spin, and statistics
of elementary excitations. Combining this knowledge and the known results on
the dynamics in the spinless CS model, we propose the expression for the
dynamical correlation functions of the SU(K) CS model. In the asymptotic
region, we confirm the consistency of our results with predictions from
conformal field theory.Comment: 22 pages, REVTe
Fractional Exclusion Statistics for the Multicomponent Sutherland Model
We show by microscopic calculation that thermodynamics of the multicomponent
Sutherland model is equivalent to that of a free particle system with
fractional exclusion statistics at all temperatures. The parameters for
exclusion statistics are given by the strength of the repulsive interaction,
and have both intra- and inter-species components. We also show that low
temperature properties of the system are described in terms of free fractional
particles without the statistical parameters for different species. The
effective exclusion statistics for intra-species at low temperatures depend on
polarization of the system.Comment: 13 pages, using RevTex, 5 figures on reques
Spin-Charge Separation at Finite Temperature in the Supersymmetric t-J Model with Long-Range Interactions
Thermodynamics is derived rigorously for the 1D supersymmetric {\it t-J}
model and its SU() generalization with inverse-square exchange. The system
at low temperature is described in terms of spinons, antispinons, holons and
antiholons obeying fractional statistics. They are all free and make the spin
susceptibility independent of electron density, and the charge susceptibility
independent of magnetization. Thermal spin excitations responsible for the
entropy of the SU() model are ascribed to free para-fermions of order
.Comment: 10 pages, REVTE
Exact dynamical structure factor of the degenerate Haldane-Shastry model
The dynamical structure factor of the K-component (K = 2,3,4)
spin chain with the 1/r^2 exchange is derived exactly at zero temperature for
arbitrary size of the system. The result is interpreted in terms of a free
quasi-particle picture which is generalization of the spinon picture in the
SU(2) case; the excited states consist of K quasi-particles each of which is
characterized by a set of K-1 quantum numbers. Divergent singularities of
at the spectral edges are derived analytically. The analytic
result is checked numerically for finite systems.Comment: 4 pages, 1 figure, accepted for publication in Phys. Rev. Let
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