301 research outputs found
Review of AdS/CFT Integrability, Chapter I.3: Long-range spin chains
In this contribution we briefly review recent developments in the theory of
long-range integrable spin chains. These spin chains constitute a natural
generalisation of the well-studied integrable nearest-neighbour chains and are
of particular relevance to the integrability in the AdS/CFT correspondence
since the dilatation operator in the asymptotic region is conjectured to be a
Hamiltonian of an integrable long-range psu spin chain.Comment: 17 pages, see also overview article arXiv:1012.3982, v2: references
to other chapters updated, v3: minor typos corrected, references adde
From the quantum Jacobi-Trudi and Giambelli formula to a nonlinear integral equation for thermodynamics of the higher spin Heisenberg model
We propose a nonlinear integral equation (NLIE) with only one unknown
function, which gives the free energy of the integrable one dimensional
Heisenberg model with arbitrary spin. In deriving the NLIE, the quantum
Jacobi-Trudi and Giambelli formula (Bazhanov-Reshetikhin formula), which gives
the solution of the T-system, plays an important role. In addition, we also
calculate the high temperature expansion of the specific heat and the magnetic
susceptibility.Comment: 18 pages, LaTeX; some explanations, 2 figures, one reference added;
typos corrected; to appear in J. Phys. A: Math. Ge
Complex Analysis of a Piece of Toda Lattice
We study a small piece of two dimensional Toda lattice as a complex dynamical
system. In particular the Julia set, which appears when the piece is deformed,
is shown analytically how it disappears as the system approaches to the
integrable limit.Comment: 17 pages, LaTe
Spinons in Magnetic Chains of Arbitrary Spins at Finite Temperatures
The thermodynamics of solvable isotropic chains with arbitrary spins is
addressed by the recently developed quantum transfer matrix (QTM) approach. The
set of nonlinear equations which exactly characterize the free energy is
derived by respecting the physical excitations at T=0, spinons and RSOS kinks.
We argue the implication of the present formulation to spinon character formula
of level k=2S SU(2) WZWN model .Comment: 25 pages, 8 Postscript figures, Latex 2e,uses graphicx, added figures
and detailed discussion
Exact solution of Calogero model with competing long-range interactions
An integrable extension of the Calogero model is proposed to study the
competing effect of momentum dependent long-range interaction over the original
{1 \ov r^2} interaction. The eigenvalue problem is exactly solved and the
consequences on the generalized exclusion statistics, which appears to differ
from the exchange statistics, are analyzed. Family of dual models with
different coupling constants is shown to exist with same exclusion statistics.Comment: Revtex, 6 pages, 1 figure, hermitian variant of the model included,
final version to appear in Phys. Rev.
A Symmetric Generalization of Linear B\"acklund Transformation associated with the Hirota Bilinear Difference Equation
The Hirota bilinear difference equation is generalized to discrete space of
arbitrary dimension. Solutions to the nonlinear difference equations can be
obtained via B\"acklund transformation of the corresponding linear problems.Comment: Latex, 12 pages, 1 figur
Dual Resonance Model Solves the Yang-Baxter Equation
The duality of dual resonance models is shown to imply that the four point
string correlation function solves the Yang-Baxter equation. A reduction of
transfer matrices to symmetry is described by a restriction of the KP
function to Toda molecules.Comment: 10 pages, LaTe
Two-State Spectral-Free Solutions of Frenkel-Moore Simplex Equation
Whilst many solutions have been found for the Quantum Yang-Baxter Equation
(QYBE), there are fewer known solutions available for its higher dimensional
generalizations: Zamolodchikov's tetrahedron equation (ZTE) and Frenkel and
Moore's simplex equation (FME). In this paper, we present families of solutions
to FME which may help us to understand more about higher dimensional
generalization of QYBE.Comment: LaTeX file. Require macros: cite.sty and subeqnarray.sty to process.
To appear in J. Phys. A: Math. and Ge
Continuous Matrix Product Ansatz for the One-Dimensional Bose Gas with Point Interaction
We study a matrix product representation of the Bethe ansatz state for the
Lieb-Linger model describing the one-dimensional Bose gas with delta-function
interaction. We first construct eigenstates of the discretized model in the
form of matrix product states using the algebraic Bethe ansatz. Continuous
matrix product states are then exactly obtained in the continuum limit with a
finite number of particles. The factorizing -matrices in the lattice model
are indispensable for the continuous matrix product states and lead to a marked
reduction from the original bosonic system with infinite degrees of freedom to
the five-vertex model.Comment: 5 pages, 1 figur
The determinant representation for quantum correlation functions of the sinh-Gordon model
We consider the quantum sinh-Gordon model in this paper. Using known formulae
for form factors we sum up all their contributions and obtain a closed
expression for a correlation function. This expression is a determinant of an
integral operator. Similar determinant representations were proven to be useful
not only in the theory of correlation functions, but also in the matrix models.Comment: 21 pages, Latex, no figure
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