650 research outputs found
Exact solution and spectral flow for twisted Haldane-Shastry model
The exact solution of the spin chain model with exchange is found for
twisted boundary conditions. The spectrum thus obtained can be reproduced by
the asymptotic Bethe ansatz. The spectral flow of each eigenstate is determined
exactly as a function of the twist angle. We find that the period for
the ground state nicely fits in with the notion of fractional exclusion
statistics.Comment: 4 pages, revtex, 1 figure available on request, to appear in PR
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
Spectral flow in the supersymmetric - model with a interaction
The spectral flow in the supersymmetric {\it t-J} model with
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
Fermionic R-Operator and Algebraic Structure of 1D Hubbard Model: Its application to quantum transfer matrix
The algebraic structure of the 1D Hubbard model is studied by means of the
fermionic R-operator approach. This approach treats the fermion models directly
in the framework of the quantum inverse scattering method. Compared with the
graded approach, this approach has several advantages. First, the global
properties of the Hamiltonian are naturally reflected in the algebraic
properties of the fermionic R-operator. We want to note that this operator is a
local operator acting on fermion Fock spaces. In particular, SO(4) symmetry and
the invariance under the partial particle hole transformation are discussed.
Second, we can construct a genuinely fermionic quantum transfer transfer matrix
(QTM) in terms of the fermionic R-operator. Using the algebraic Bethe Ansatz
for the Hubbard model, we diagonalize the fermionic QTM and discuss its
properties.Comment: 22 pages, no 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
A Solvable Model of Interacting Fermions in Two Dimensions
We introduce and study an exactly solvable model of several species of
fermions in which particles interact pairwise through a mutual magnetic field;
the interaction operates only between particles belonging to different species.
After an unitary transformation, the model reduces to one in which each
particle sees a magnetic field which depends on the total numbers of particles
of all the other species; this may be viewed as the mean-field model for a
class of anyonic theories. Our model is invariant under charge conjugation C
and the product PT (parity and time reversal). For the special case of two
species, we examine various properties of this system, such as the Hall
conductivity, the wave function overlap arising from the transfer of one
particle from one species to another, and the one-particle off-diagonal density
matrix. Our model is a generalization of a recently introduced solvable model
in one dimension.Comment: Revtex, 7 page
Two-Triplet-Dimer Excitation Spectra in the Shastry-Sutherland Model for SrCu_2(BO_3)_2
By using the perturbation expansion up to the fifth order, we study the
two-triplet-dimer excitation spectra in the Shastry-Sutherland model, where the
localized nature of a triplet-dimer, the propagation of a triplet-dimer pair by
the correlated hopping and the long-range interactions between triplet-dimers
play an essential role. It is found that the dispersion relations for
first-neighbor triplet-dimer pair excitations with S=1 and p-type symmetry
qualitatively explain the second-lowest branch observed in the neutron
inelastic scattering experiment. It is also predicted that the second-lowest
branch consists of two components, p_x- and p_y-states, with slightly different
excitation energies. The origin of the singlet mode at 3.7meV observed in the
Raman scattering experiment is also discussed.Comment: 5 pages, 3 figure
Dynamical Structure Factors of the Spin-1/2 XXZ Chain with Inverse-Square Exchange and Ising Anisotropy
The dynamical properties of the S=1/2 antiferromagnetic XXZ chain are studied
by the exact diagonalization and the recursion method of finite systems up to
24 sites. Two types of the exchange interaction are considered: one is the
nearest-neighbor type, and the other is the inverse-square one. As the Ising
anisotropy becomes larger, there appears a noticeable difference in the
transverse component S^{xx}(q,\omega) between the two types of the exchange.
For the nearest-neighbor type, the peak frequency of S^{xx}(q,\omega) for each
q approaches the center of the continuum spectrum. On the contrary, the peak
frequency for the inverse-square type moves to the upper edge of the continuum,
and separates from the continuum for the anisotropy larger than the threshold
value. Whether the interaction between domain walls (solitons) is absent or
repulsive in the Ising limit leads to this difference in the behavior of
S^{xx}(q,\omega). In the longitudinal component S^{zz}(q,\omega), on the other
hand, the feature of the dynamics is scarcely different between the two types.
The energy gap and the static properties are also discussed.Comment: 10 pages. A hard copy of 16 figures is available on request.
Submitted to J. Phys. Soc. Jp
Theory of Orbital Ordering, Fluctuation and Resonant X-ray Scattering in Manganites
A theory of resonant x-ray scattering in perovskite manganites is developed
by applying the group theory to the correlation functions of the pseudospin
operators for the orbital degree of freedom. It is shown that static and
dynamical informations of the orbital state are directly obtained from the
elastic, diffuse and inelastic scatterings due to the tensor character of the
scattering factor. We propose that the interaction and its anisotropy between
orbitals are directly identified by the intensity contour of the diffuse
scattering in the momentum space.Comment: 4 pages, 1 figur
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