584 research outputs found
Irreducibility of fusion modules over twisted Yangians at generic point
With any skew Young diagram one can associate a one parameter family of
"elementary" modules over the Yangian \Yg(\g\l_N). Consider the twisted
Yangian \Yg(\g_N)\subset \Yg(\g\l_N) associated with a classical matrix Lie
algebra \g_N\subset\g\l_N. Regard the tensor product of elementary Yangian
modules as a module over \Yg(\g_N) by restriction. We prove its
irreducibility for generic values of the parameters.Comment: Replaced with journal version, 18 page
A Labelling Scheme for Higher Dimensional Simplex Equations
We present a succinct way of obtaining all possible higher dimensional
generalization of Quantum Yang-Baxter Equation (QYBE). Using the scheme, we
could generate the two popular three-simplex equations, namely: Zamolodchikov's
tetrahedron equation (ZTE) and Frenkel and Moore equation (FME).Comment: To appear as a Letter to the Editor in J. Phys. A:Math and Ge
On classical q-deformations of integrable sigma-models
JHEP is an open-access journal funded by SCOAP3 and licensed under CC BY 4.0A procedure is developed for constructing deformations of integrable σ-models which are themselves classically integrable. When applied to the principal chiral model on any compact Lie group F, one recovers the Yang-Baxter σ-model introduced a few years ago by C. Klimčík. In the case of the symmetric space σ-model on F/G we obtain a new one-parameter family of integrable σ-models. The actions of these models correspond to a deformation of the target space geometry and include a torsion term. An interesting feature of the construction is the q-deformation of the symmetry corresponding to left multiplication in the original models, which becomes replaced by a classical q-deformed Poisson-Hopf algebra. Another noteworthy aspect of the deformation in the coset σ-model case is that it interpolates between a compact and a non-compact symmetric space. This is exemplified in the case of the SU(2)/U(1) coset σ-model which interpolates all the way to the SU(1, 1)/U(1) coset σ-modelPeer reviewedFinal Published versio
On algebraic structures in supersymmetric principal chiral model
Using the Poisson current algebra of the supersymmetric principal chiral
model, we develop the algebraic canonical structure of the model by evaluating
the fundamental Poisson bracket of the Lax matrices that fits into the rs
matrix formalism of non-ultralocal integrable models. The fundamental Poisson
bracket has been used to compute the Poisson bracket algebra of the monodromy
matrix that gives the conserved quantities in involution
Domain wall partition functions and KP
We observe that the partition function of the six vertex model on a finite
square lattice with domain wall boundary conditions is (a restriction of) a KP
tau function and express it as an expectation value of charged free fermions
(up to an overall normalization).Comment: 16 pages, LaTeX2
The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
The longitudinal spin structure factor for the XXZ-chain at small wave-vector
q is obtained using Bethe Ansatz, field theory methods and the Density Matrix
Renormalization Group. It consists of a peak with peculiar, non-Lorentzian
shape and a high-frequency tail. We show that the width of the peak is
proportional to q^2 for finite magnetic field compared to q^3 for zero field.
For the tail we derive an analytic formula without any adjustable parameters
and demonstrate that the integrability of the model directly affects the
lineshape.Comment: 4 pages, 3 figures, published versio
Permutation-type solutions to the Yang-Baxter and other n-simplex equations
We study permutation type solutions to n-simplex equations, that is,
solutions whose R matrix can be written as a product of delta- functions
depending linearly on the indices. With this ansatz the D^{n(n+1)} equations of
the n-simplex equation reduce to an [n(n+1)/2+1]x[n(n+1)/2+1] matrix equation
over Z_D. We have completely analyzed the 2-, 3- and 4-simplex equations in the
generic D case. The solutions show interesting patterns that seem to continue
to still higher simplex equations.Comment: 20 pages, LaTeX2e. to appear in J. Phys. A: Math. Gen. (1997
Time-dependent correlation function of the Jordan-Wigner operator as a Fredholm determinant
We calculate a correlation function of the Jordan-Wigner operator in a class
of free-fermion models formulated on an infinite one-dimensional lattice. We
represent this function in terms of the determinant of an integrable Fredholm
operator, convenient for analytic and numerical investigations. By using Wick's
theorem, we avoid the form-factor summation customarily used in literature for
treating similar problems.Comment: references added, introduction and conclusion modified, version
accepted for publication in J. Stat. Mec
Classical integrability of Schrodinger sigma models and q-deformed Poincare symmetry
We discuss classical integrable structure of two-dimensional sigma models
which have three-dimensional Schrodinger spacetimes as target spaces. The
Schrodinger spacetimes are regarded as null-like deformations of AdS_3. The
original AdS_3 isometry SL(2,R)_L x SL(2,R)_R is broken to SL(2,R)_L x U(1)_R
due to the deformation. According to this symmetry, there are two descriptions
to describe the classical dynamics of the system, 1) the SL(2,R)_L description
and 2) the enhanced U(1)_R description. In the former 1), we show that the
Yangian symmetry is realized by improving the SL(2,R)_L Noether current. Then a
Lax pair is constructed with the improved current and the classical
integrability is shown by deriving the r/s-matrix algebra. In the latter 2), we
find a non-local current by using a scaling limit of warped AdS_3 and that it
enhances U(1)_R to a q-deformed Poincare algebra. Then another Lax pair is
presented and the corresponding r/s-matrices are also computed. The two
descriptions are equivalent via a non-local map.Comment: 20 pages, no figure, further clarification and references adde
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