Related papers: Towards Three-Dimensional Bethe Ansatz
The problem of diagonalization of the quantum mechanical Hamiltonian, governing dynamics of an electron on a two-dimensional triangular or square lattice in external uniform magnetic field, applied perpendicularly to the lattice plane, the…
An analytic Bethe ansatz is carried out related to the type 1 Lie superalgebra C(s). We present eigenvalue formulae of transfer matrices in dressed vacuum form (DVF) labeled by Young superdiagrams with one row or one column. We also propose…
We investigate Bethe Ansatz equations for the one-dimensional spin-$\frac{1}{2}$ Heisenberg XXX chain with a special interest in a finite system. Solutions for the two-particle sector are obtained. The ground state in antiferromagnetic case…
Eigenvalues of the commuting family of transfer matrices are expected to obey the $T$-system, a set of functional relation, proposed recently. Here we obtain the solution to the $T$-system for $C^{(1)}_2$ vertex models. They are compatible…
We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $\mathfrak{gl}_3$-invariant $R$-matrix. We study a new recently proposed approach to construct on-shell Bethe vectors of these models. We…
In the theory of Bethe-ansatz integrable quantum systems, rapidities play an important role as they are used to specify many-body states, apart from phases. The physical interpretation of rapidities going back to Sutherland is that they are…
In this text, we provide a detailed exposition of the Algebraic Bethe ansatz for square ice (or six vertex model), which allows the construction of candidate eigenvectors for the transfer matrices of this model. We also prove some formula…
We review the algebraic Bethe ansatz for the Heisenberg model. The exposition includes some of recent advancements with emphasis on a relation with the rigged configurations. We also provide somewhat thorough review of the crystal bases and…
A generalization of the eight vertex model by means of higher spin representations of the Sklyanin algebra is investigated by the quantum inverse scattering method and the algebraic Bethe Ansatz. Under the well-known string hypothesis…
We give a review of some recent work on generalization of the Bethe ansatz in the case of $2+1$-dimensional models of quantum field theory. As such a model, we consider one associated with the tetrahedron equation, i.e. the…
New variables of separation for few integrable systems on the two-dimensional sphere with higher order integrals of motion are considered in detail. We explicitly describe canonical transformations of initial physical variables to the…
In this paper and upcoming ones, we initiate a systematic study of Bethe ansatz equations for integrable models by modern computational algebraic geometry. We show that algebraic geometry provides a natural mathematical language and…
We observe that the exactly solved eight-vertex solid-on-solid model contains an hitherto unnoticed arbitrary field parameter, similar to the horizontal field in the six-vertex model. The parameter is required to describe a continuous…
We apply the nested algebraic Bethe ansatz to a model of one-dimensional two-component Bose gas with delta-function repulsive interaction. Using a lattice approximation of the L-operator we find Bethe vectors of the model in the continuous…
Having introduced the magnon in part I and the spinon in part II as the relevant quasi-particles for the interpretation of the spectrum of low-lying excitations in the one-dimensional (1D) s=1/2 Heisenberg ferromagnet and antiferromagnet,…
The aim of the chapter is to introduce in a pedagogical manner the concept of Thermodynamic Bethe Ansatz designed to calculate the energy levels of finite volume integrable systems and to review how it is applied in the planar AdS/CFT…
The exact solution of the one-dimensional super-symmetric t-J model under generic integrable boundary conditions is obtained via the Bethe ansatz methods. With the coordinate Bethe ansatz, the corresponding R-matrix and K-matrices are…
The Bethe ansatz for the one-dimensional s=1/2 Heisenberg ferromagnet is introduced at an elementary level. The presentation follows Bethe's original work very closely. A detailed description and a complete classification of all two-magnon…
Let $H$ be the Hilbert scheme of curves in complex projective $3$-space, with $d\geq 3$ and genus $g \leq (d-2)^2/4$. A complete, explicit description of the cone of curves and the ample cone of $H$ is given. From this, partial results on…
We develop a method for finding the time evolution of exactly solvable models by Bethe ansatz. The dynamical Bethe wavefunction takes the same form as the stationary Bethe wavefunction except for time varying Bethe parameters and a complex…