6,959 research outputs found
Schlesinger transformations for elliptic isomonodromic deformations
Schlesinger transformations are discrete monodromy preserving symmetry
transformations of the classical Schlesinger system. Generalizing well-known
results from the Riemann sphere we construct these transformations for
isomonodromic deformations on genus one Riemann surfaces. Their action on the
system's tau-function is computed and we obtain an explicit expression for the
ratio of the old and the transformed tau-function.Comment: 19 pages, LaTeX2
Anomalous magnetization process in frustrated spin ladders
We study, at T=0, the anomalies in the magnetization curve of the S=1 two-leg
ladder with frustrated interactions. We focus mainly on the existence of the
M=\Ms/2 plateau, where \Ms is the saturation magnetization. We use
analytical methods (degenerate perturbation theory and non-Abelian
bosonization) as well as numerical methods (level spectroscopy and density
matrix renormalization group), which lead to the consistent conclusion with
each other. We also touch on the M=\Ms/4 and M=(3/4)\Ms plateaux and cusps.Comment: 4 pages, 7 figures (embedded), Conference paper (Highly Frustrated
Magnetism 2003, 26-30th August 2003, Grenoble, France
A remark on the Hankel determinant formula for solutions of the Toda equation
We consider the Hankel determinant formula of the functions of the
Toda equation. We present a relationship between the determinant formula and
the auxiliary linear problem, which is characterized by a compact formula for
the functions in the framework of the KP theory. Similar phenomena that
have been observed for the Painlev\'e II and IV equations are recovered. The
case of finite lattice is also discussed.Comment: 14 pages, IOP styl
Magnetic properties of the distorted diamond chain at T=0
We explore, at T=0, the magnetic properties of the antiferromagnetic
distorted diamond chain described by the Hamiltonian {\cal H}
= \sum_{j=1}^{N/3}{J_1 ({\bi S}_{3j-1} \cdot {\bi S}_{3j}
+ {\bi S}_{3j} \cdot {\bi S}_{3j+1})
+ J_2 {\bi S}_{3j+1} \cdot {\bi S}_{3j+2}
+ J_3 ({\bi S}_{3j-2} \cdot {\bi S}_{3j}
+ {\bi S}_{3j} \cdot {\bi S}_{3j+2})}
\allowbreak - H \sum_{l=1}^{N} S_l^z with , which well
models with , and azurite . We employ the physical
consideration, the degenerate perturbation theory, the level spectroscopy
analysis of the numerical diagonalization data obtained by the Lanczos method
and also the density matrix renormalization group (DMRG) method. We investigate
the mechanisms of the magnetization plateaux at and , and
also show the precise phase diagrams on the plane
concerning with these magnetization plateaux, where
and is the saturation magnetization. We also calculate the magnetization
curves and the magnetization phase diagrams by means of the DMRG method.Comment: 21 pages, 29 figure
Field-Induced gap due to four-spin exchange in a spin ladder
The effect of the four-spin cyclic exchange interaction at each plaquette in
the two-leg spin ladder is investigated at T=0, especially focusing on
the field-induced gap. The strong rung coupling approximation suggests that it
yields a plateau at half of the saturation moment () in the
magnetization curve, which corresponds to a field-induced spin gap with a
spontaneous breaking of the translational symmetry. A precise phase diagram at
is also presented based on the level spectroscopy analysis of the
numerical data obtained by Lanczos method. The boundary between the gapless and
plateau phases is confirmed to be of the Kosterlitz-Thouless (KT) universality
class.Comment: 10 pages, 3 eps figures (embedded), to be published in J. Phys.:
Cond. Matte
Band-Insulator-Metal-Mott-Insulator transition in the half--filled ionic-Hubbard chain
We investigate the ground state phase diagram of the half-filled
repulsive Hubbard model in the presence of a staggered ionic
potential , using the continuum-limit bosonization approach. We find,
that with increasing on-site-repulsion , depending on the value of the
next-nearest-hopping amplitude , the model shows three different
versions of the ground state phase diagram. For , the ground state phase diagram consists of the following
three insulating phases: Band-Insulator at , Ferroelectric Insulator
at . For
there is only one transition from a spin gapped
metallic phase at .
Finally, for intermediate values of the next-nearest-hopping amplitude
we find that with increasing
on-site repulsion, at the model undergoes a second-order
commensurate-incommensurate type transition from a band insulator into a
metallic state and at larger there is a Kosterlitz-Thouless type
transition from a metal into a ferroelectric insulator.Comment: 9 pages 3 figure
On the Linearization of the Painleve' III-VI Equations and Reductions of the Three-Wave Resonant System
We extend similarity reductions of the coupled (2+1)-dimensional three-wave
resonant interaction system to its Lax pair. Thus we obtain new 3x3 matrix
Fuchs--Garnier pairs for the third and fifth Painleve' equations, together with
the previously known Fuchs--Garnier pair for the fourth and sixth Painleve'
equations. These Fuchs--Garnier pairs have an important feature: they are
linear with respect to the spectral parameter. Therefore we can apply the
Laplace transform to study these pairs. In this way we found reductions of all
pairs to the standard 2x2 matrix Fuchs--Garnier pairs obtained by M. Jimbo and
T. Miwa. As an application of the 3x3 matrix pairs, we found an integral
auto-transformation for the standard Fuchs--Garnier pair for the fifth
Painleve' equation. It generates an Okamoto-like B\"acklund transformation for
the fifth Painleve' equation. Another application is an integral transformation
relating two different 2x2 matrix Fuchs--Garnier pairs for the third Painleve'
equation.Comment: Typos are corrected, journal and DOI references are adde
Magnetization Plateau of an S=1 Frustrated Spin Ladder
We study the magnetization plateau at 1/4 of the saturation magnetization of
the S=1 antiferromagnetic spin ladder both analytically and numerically, with
the aim of explaining recent experimental results on BIP-TENO by Goto et al. We
propose two mechanisms for the plateau formation and clarify the plateau phase
diagram on the plane of the coupling constants between spins
Integrable theory of quantum transport in chaotic cavities
The problem of quantum transport in chaotic cavities with broken
time-reversal symmetry is shown to be completely integrable in the universal
limit. This observation is utilised to determine the cumulants and the
distribution function of conductance for a cavity with ideal leads supporting
an arbitrary number of propagating modes. Expressed in terms of solutions
to the fifth Painlev\'e transcendent and/or the Toda lattice equation, the
conductance distribution is further analysed in the large- limit that
reveals long exponential tails in the otherwise Gaussian curve.Comment: 4 pages; final version to appear in Physical Review Letter
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