75 research outputs found
On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain
We consider the problem of computing form factors of the massless XXZ
Heisenberg spin-1/2 chain in a magnetic field in the (thermodynamic) limit
where the size M of the chain becomes large. For that purpose, we take the
particular example of the matrix element of the third component of spin between
the ground state and an excited state with one particle and one hole located at
the opposite ends of the Fermi interval (umklapp-type term). We exhibit its
power-law decrease in terms of the size of the chain M, and compute the
corresponding exponent and amplitude. As a consequence, we show that this form
factor is directly related to the amplitude of the leading oscillating term in
the long-distance asymptotic expansion of the two-point correlation function of
the third component of spin.Comment: 28 page
Exact Ground States in Spin Systems with Orbital Degeneracy
We present exact ground states in spin models with orbital generacy in one
and higher dimensions. A method to obtain the exact ground states of the models
when the Hamiltonians are composed of the products of two commutable operators
is proposed. For the case of the spin-1/2 model with two-fold degeneracy some
exact ground states are given, such as the Valence-Bond (VB), the magnetically
ordered, and the orbitally ordered states under particular parameter regimes.
We also find the models with the higher spin and degeneracy which have the new
types of VB ground states in the spin and the orbital sectors.Comment: 4 pages(JPSJ.sty), 2 figures(EPS), to appear in J. Phys. Soc. Jpn.
68, No.2 (1999) 32
axial form factor from bubble chamber experiments
A careful reanalysis of both Argonne National Laboratory and Brookhaven
National Laboratory data for weak single pion production is done. We consider
deuteron nuclear effects and normalization (flux) uncertainties in both
experiments. We demonstrate that these two sets of data are in good agreement.
For the dipole parametrization of , we obtain , GeV. As an application we present the discussion of
the uncertainty of the neutral current 1 production cross section,
important for the T2K neutrino oscillation experiment.Comment: 16 pages, 8 figures, 2 table
Three-leg Antiferromagnetic Heisenberg Ladder with Frustrated Boundary Condition; Ground State Properties
The antiferromagnetic Heisenberg spin systems on the three-leg ladder are
investigated. Periodic boundary condition is imposed in the rung direction. The
system has an excitation gap for all antiferromagnetic inter-chain coupling
(). The estimated gap for the strong coupling limit
() is 0.28. Although the interaction is
homogeneous and only nearest-neighbor, the ground states of the system are
dimerized and break the translational symmetry in the thermodynamic limit.
Introducing the next-nearest neighbor coupling (), we can see that the
system is solved exactly. The ground state wave function is completely
dimer-ordered. Using density matrix renomalization group algorithm, we show
numerically that the original model () has the same nature with the
exactly solvable model. The ground state properties of the ladder with a higher
odd number of legs are also discussed.Comment: 15 pages, LaTeX, to be published in J.Phys.Soc.Jpn. Vol. 66 No. 1
Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables
The antiperiodic transfer matrix associated to higher spin representations of
the rational 6-vertex Yang-Baxter algebra is analyzed by generalizing the
approach introduced recently in [1], for the cyclic representations, in [2],
for the spin-1/2 highest weight representations, and in [3], for the spin 1/2
representations of the reflection algebra. Here, we derive the complete
characterization of the transfer matrix spectrum and we prove its simplicity in
the framework of Sklyanin's quantum separation of variables (SOV). Then, the
characterization of local operators by Sklyanin's quantum separate variables
and the expression of the scalar products of separates states by determinant
formulae allow to compute the form factors of the local spin operators by one
determinant formulae similar to the scalar product ones. Finally, let us
comment that these results represent the SOV analogous in the antiperiodic
higher spin XXX quantum chains of the results obtained for the periodic chains
in [4] in the framework of the algebraic Bethe ansatz.Comment: 20 pages, introduction improved by taking into account some relevant
references on the spectrum of the model under general boundary conditions, no
further relevant modification
Generalized Valence Bond State and Solvable Models for Spin-1/2 Systems with Orbital degeneracy
A spin-1/2 system with double orbital degeneracy may possess SU(4) symmetry.
According to the group theory a global SU(4) singelt state can be expressed as
a linear combination of all possible configurations consisting of four-site
SU(4) singlets. Following P. W. Andersion's idea for spin 1/2 system, we
propose that the ground state for the antiferromagnetic SU(4) model is SU(4)
resonating valence bond (RVB) state. A short-range SU(4) RVB state is a spin
and orbital liquid, and its elementary excitations has an energy gap. We
construct a series of solvale models which ground states are short-range SU(4)
RVB states. The results can be generalized to the antiferromagnetic SU(N)
models.Comment: 4 page
Fine Structure and Fractional Aharonov-Bohm Effect
We find a fine structure in the Aharonov-Bohm effect, characterized by the
appearence of a new type of periodic oscillations having smaller fractional
period and an amplitude, which may compare with the amplitude of the
conventional Aharonov-Bohm effect. Specifically, at low density or strong
coupling on a Hubbard ring can coexist along with the conventional Aaronov-Bohm
oscillations with the period equal to an integer, measured in units of the
elementary flux quantum, two additional oscillations with periods and
. The integers and are the particles number and the number of
down-spin particles, respectively. {}From a solution of the Bethe ansatz
equations for electrons located on a ring in a magnetic field we show that
the fine structure is due to electron-electron and Zeeman interactions. Our
results are valid in the dilute density limit and for an arbitrary value of the
Hubbard repulsion Comment: 40 pages (Latex,Revtex) 12 figures by request, in Technical Reports
of ISSP , Ser. A, No.2836 (1994
Tricritical Behavior in the Extended Hubbard Chains
Phase diagrams of the one-dimensional extended Hubbard model (including
nearest-neighbor interaction ) at half- and quarter-filling are studied by
observing level crossings of excitation spectra using the exact
diagonalization. This method is based on the Tomonaga-Luttinger liquid theory
including logarithmic corrections which stem from the renormalization of the
Umklapp- and the backward-scattering effects.
Using this approach, the phase boundaries are determined with high accuracy,
and then the structure of the phase diagram is clarified. At half-filling, the
phase diagram consists of two
Berezinskii-Kosterlitz-Thouless (BKT) transition lines and one Gaussian
transition line in the charge sector, and one spin-gap transition line.
This structure reflects the U(1) SU(2) symmetry of the electron
system. Near the line, the Gaussian and the spin-gap transitions take
place independently from the weak- to the intermediate-coupling region, but
these two transition lines are coupled in the strong-coupling region. This
result demonstrates existence of a tricritical point and a
bond-charge-density-wave (BCDW) phase between charge- and spin-density-wave
(CDW, SDW) phases. To clarify this mechanism of the transition, we also
investigate effect of a correlated hopping term which plays a role to enlarge
BCDW and bond-spin-density-wave (BSDW) phases. At quarter-filling, a similar
crossover phenomenon also takes place in the large- region involving
spin-gap and BKT-type metal-insulator transitions.Comment: 18 pages(REVTeX), 17 figures(EPS(color)), 3 tables, Detailed paper of
JPSJ 68 (1999) 3123 (cond-mat/9903227), see also cond-mat/000341
Antiperiodic dynamical 6-vertex model I: Complete spectrum by SOV, matrix elements of the identity on separate states and connections to the periodic 8-vertex model
The spin-1/2 highest weight representations of the dynamical 6-vertex and the
standard 8-vertex Yang-Baxter algebra on a finite chain are considered in this
paper. For the antiperiodic dynamical 6-vertex transfer matrix defined on
chains with an odd number of sites, we adapt the Sklyanin's quantum separation
of variable (SOV) method and explicitly construct SOV representations from the
original space of representations. We provide the complete characterization of
eigenvalues and eigenstates proving also the simplicity of its spectrum.
Moreover, we characterize the matrix elements of the identity on separated
states by determinant formulae. The matrices entering in these determinants
have elements given by sums over the SOV spectrum of the product of the
coefficients of separate states. This SOV analysis is not reduced to the case
of the elliptic roots of unit and the results here derived define the required
setup to extend to the dynamical 6-vertex model the approach recently developed
in [1]-[5] to compute the form factors of the local operators in the SOV
framework, these results will be presented in a future publication. For the
periodic 8-vertex transfer matrix, we prove that its eigenvalues have to
satisfy a fixed system of equations. In the case of a chain with an odd number
of sites, this system of equations is the same entering in the SOV
characterization of the antiperiodic dynamical 6-vertex transfer matrix
spectrum. This implies that the set of the periodic 8-vertex eigenvalues is
contained in the set of the antiperiodic dynamical 6-vertex eigenvalues. A
criterion is introduced to find simultaneous eigenvalues of these two transfer
matrices and associate to any of such eigenvalues one nonzero eigenstate of the
periodic 8-vertex transfer matrix by using the SOV results. Moreover, a
preliminary discussion on the degeneracy of the periodic 8-vertex spectrum is
also presented.Comment: 36 pages, main modifications in section 3 and one appendix added, no
result modified for the dynamical 6-vertex transfer matrix spectrum and the
matrix elements of identity on separate states for chains with an odd number
of site
Reaction and Axial Vector Coupling
The reaction is studied in the region of low
to investigate the effect of deuteron structure and width of the
resonance on the differential cross section. The results are used to extract
the axial vector coupling from the experimental data on
this reaction. The possibility to determine this coupling from electroweak
interaction experiments with high intensity electron accelerators is discussed.Comment: 14 pages, REVTEX, 5 figure
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