158 research outputs found
On the Integrability of Classical Ruijsenaars-Schneider Model of Type
The problem of finding most general form of the classical integrable
relativistic models of many-body interaction of the type is
considered. In the simplest nontrivial case of ,the extra integral of
motion is presented in explicit form within the ansatz similar to the
nonrelativistic Calogero-Moser models. The resulting Hamiltonian has been found
by solving the set of two functional equations.Comment: 10 pages, LaTeX2e, no figure
On the spectrum of S=1/2 XXX Heisenberg chain with elliptic exchange
It is found that the Hamiltonian of S=1/2 isotropic Heisenberg chain with
sites and elliptic non-nearest-neighbor exchange is diagonalized in each sector
of the Hilbert space with magnetization , , by means of
double quasiperiodic meromorphic solutions to the -particle quantum
Calogero-Moser problem on a line. The spectrum and highest-weight states are
determined by the solutions of the systems of transcendental equations of the
Bethe-ansatz type which arise as restrictions to particle pseudomomenta.Comment: 9 pages, Late
On the two-magnon bound states for the quantum Heisenberg chain with variable range exchange
The spectrum of finite-difference two-magnon operator is investigated for
quantum S=1/2 chain with variable range exchange of the form . It is found that usual bound state appears for some values
of the total pseudomomentum of two magnons as for the Heisenberg chain with
nearest-neighbor spin interaction. Besides this state, a new type of bound
state with oscillating wave function appears at larger values of the total
pseudomomentum.Comment: 8 pages, latex, no figure
New Family of Solvable 1D Heisenberg Models
Starting from a Calogero--Sutherland model with hyperbolic interaction
confined by an external field with Morse potential we construct a Heisenberg
spin chain with exchange interaction on a lattice given
in terms of the zeroes of Laguerre polynomials. Varying the strength of the
Morse potential the Haldane--Shastry and harmonic spin chains are reproduced.
The spectrum of the models in this class is found to be that of a classical
one-dimensional Ising chain with nonuniform nearest neighbour coupling in a
nonuniform magnetic field which allows to study the thermodynamics in the limit
of infinite chains.Comment: 8 pp, LaTeX, ITP-UH-07/9
Integrability of N=6 Chern-Simons Theory at Six Loops and Beyond
We study issues concerning perturbative integrability of N=6 Chern-Simons
theory at planar and weak `t Hooft coupling regime. By Feynman diagrammatics,
we derive so called maximal-ranged interactions in the quantum dilatation
generator, originating from homogeneous and inhomogeneous diagrams. These
diagrams require proper regularization of not only ultraviolet but also
infrared divergences. We first consider standard operator mixing method. We
show that homogeneous diagrams are obtainable by recursive method to all
orders. The method, however, is not easily extendable to inhomogeneous
diagrams. We thus consider two-point function method and study both operator
contents and spectrum of the quantum dilatation generator up to six loop
orders. We show that, of two possible classes of operators, only one linear
combination actually contributes. Curiously, this is exactly the same
combination as in N=4 super Yang-Mills theory. We then study spectrum of
anomalous dimension up to six loops. We find that the spectrum agrees perfectly
with the prediction based on quantum integrability. In evaluating the six loop
diagrams, we utilized remarkable integer-relation algorithm (PSLQ) developed by
Ferguson, Baily and Arno.Comment: 1+39 pages, 12 figures, references added, minor structural changes,
typos correcte
Chern-Simons theory, exactly solvable models and free fermions at finite temperature
We show that matrix models in Chern-Simons theory admit an interpretation as
1D exactly solvable models, paralleling the relationship between the Gaussian
matrix model and the Calogero model. We compute the corresponding Hamiltonians,
ground-state wavefunctions and ground-state energies and point out that the
models can be interpreted as quasi-1D Coulomb plasmas. We also study the
relationship between Chern-Simons theory on and a system of N
one-dimensional fermions at finite temperature with harmonic confinement. In
particular we show that the Chern-Simons partition function can be described by
the density matrix of the free fermions in a very particular, crystalline,
configuration. For this, we both use the Brownian motion and the matrix model
description of Chern-Simons theory and find several common features with c=1
theory at finite temperature. Finally, using the exactly solvable model result,
we show that the finite temperature effect can be described with a specific
two-body interaction term in the Hamiltonian, with 1D Coulombic behavior at
large separations.Comment: 19 pages, v2: references adde
Deformations of Calogero-Moser Systems
Recent results are surveyed pertaining to the complete integrability of some
novel n-particle models in dimension one. These models generalize the
Calogero-Moser systems related to classical root systems. Quantization leads to
difference operators instead of differential operators.Comment: 4 pages, Latex (version 2.09), talk given at NEEDS '93, Gallipoli,
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