Related papers: An exact solution to asymptotic Bethe equation
The general solution for the static, spherical and asymptotically flat braneworld is derived by solving the bulk Einstein equation and braneworld dynamics. We show that it involves a large arbitrariness, which reduces the predictability of…
The low temperature magnetization process of the ferromagnetic-antiferromagnetic Heisenberg chain is studied using the interacting boson approximation. In the low field regime and near the saturation field, the spin wave excitations are…
The low-lying excitations of the asymmetric $XXZ$ spin chain are derived explicitly in the antiferromagnetic regime through the Bethe Ansatz. It is found that a massless and conformal invariant phase with central charge $c=1$ is separated…
We present a family of explicit solutions for a nonlinear classical vector model with anisotropic Heisenberg-like interaction on the triangular lattice.
We solve for the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups ${\cal U}_q(X_n } for $X_n = A_1,B_n,C_n$ and $D_n$. We employ a generalization of the coordinate…
We solve the Schroedinger equation for an interacting spin-chain locally coupled to a quantum environment with a specific degeneracy structure. The reduced dynamics of the whole spin-chain as well as of single spins is analyzed. We show,…
The paper deals with a problem of asymptotic soliton like solutions to the Benjamin-Bona-Mahony (BBM) equaion with a small parameter at the highest derivative and variable coefficients depending on the variables $x$, $t$ as well as a small…
Using the Algebraic Bethe Ansatz we consider the correlation functions of the integrable higher spin chains. We apply a method recently developed for the spin $\frac 12$ Heisenberg chain, based on the solution of the quantum inverse…
It is shown that a generalization of Bethe Ansatz based on an utilization of {\it degenerative discrete-diffractive} wave functions solves the three-magnon problem for the $S=1$ isotropic ferromagnetic infinite chain. The four-magnon…
Building on the fundamentals introduced in part I, we employ the Bethe ansatz to study some ground-state properties (energy, magnetization, susceptibility) of the one-dimensional s=1/2 Heisenberg antiferromagnet in zero and nonzero magnetic…
We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Using the Bethe ansatz and similarity transformations this yields new exact…
We present a review of the method we have elaborated to compute the correlation functions of the XXZ spin-1/2 Heisenberg chain. This method is based on the resolution of the quantum inverse scattering problem in the algebraic Bethe Ansatz…
Asymptotically exact low temperature expansions for the $s=1/2$ Heisenberg XXZ chains with boundaries are implemented by using the boundary conformal field theory. It is found that for $1/2<\Delta\leq 1$, ($\Delta$, an anisotropic…
We elaborate a systematic way to obtain higher order contributions in the nonlinear steepest descent method for Riemann-Hilbert problem associated with homogeneous Painleve II equation. The problem is reformulated as a matrix factorization…
We calculate the boundary $S$ matrix for the open antiferromagnetic spin $1/2$ isotropic Heisenberg chain with boundary magnetic fields. Our approach, which starts from the model's Bethe Ansatz solution, is an extension of the…
We examine solitary waves in classical Heisenberg chains with an uniaxial anisotropy and a parallel magnetic field in a continuum approach. The boundary conditions commonly used are generalized to nonlinear spin wave states, which…
We use the functional representation of Heisenberg-Weyl group and obtain equation for the spectrum of the model, which is more complicated than Bethes ones, but can be written explicitly through theta functions.
We consider rational integrable supersymmetric gl(m|n) spin chains in the defining representation and prove the isomorphism between a commutative algebra of conserved charges (the Bethe algebra) and a polynomial ring (the Wronskian algebra)…
The $sl_q(2)$-quantum group invariant spin 1/2 XXZ-Heisenberg model with open boundary conditions is investigated by means of the Bethe ansatz. As is well known, quantum groups for $q$ equal to a root of unity possess a finite number of…
Using the Riemann-Hilbert approach, we explicitly construct the asymptotic $\Psi$-function corresponding to the solution $y\sim\pm\sqrt{-x/2}$ as $|x|\to\infty$ to the second Painlev\'e equation $y_{xx}=2y^3+xy-\alpha$. We precisely…