Related papers: Eigenvectors and scalar products for long range in…
In this note, we propose an expression for the eigenvectors and scalar products for a class of spin chains with long-range interaction and su(2) symmetry. This class includes the Inozemtsev spin chain as well as the BDS spin chain, which is…
We show that the scalar products of on-shell and off-shell Bethe vectors in the algebra1ic Bethe ansatz solvable models satisfy a system of linear equations. We find solutions to this system for a wide class of integrable models. We also…
We consider the finite volume mean values of current operators in integrable spin chains with local interactions, and provide an alternative derivation of the exact result found recently by the author and two collaborators. We use a certain…
We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes…
We present a recursion relation for the explicit construction of integrable spin chain Hamiltonians with long-range interactions. Based on arbitrary short-range (e.g. nearest-neighbor) integrable spin chains, it allows to construct an…
We study the scalar products between Bethe states in the XXZ spin chain with anisotropy $|\Delta|>1$ in the semi-classical limit where the length of the spin chain and the number of magnons tend to infinity with their ratio kept finite and…
We derive exactly scalar products and form factors for integrable higher-spin XXZ chains through the algebraic Bethe-ansatz method. Here spin values are arbitrary and different spins can be mixed. We show the affine quantum-group symmetry,…
A quantum algebra invariant integrable closed spin 1 chain is introduced and analysed in detail. The Bethe ansatz equations as well as the energy eigenvalues of the model are obtained. The highest weight property of the Bethe vectors with…
We consider an $XYZ$ spin chain within the framework of the generalized algebraic Bethe ansatz. We study scalar products of the transfer matrix eigenvectors and arbitrary Bethe vectors. In the particular case of free fermions we obtain…
We present new integrable models of interacting spin-1/2 chains, which can be interpreted as hard rod deformations of the XXZ Heisenberg chains. The models support multiple particle types: dynamical hard rods of length $\ell$ and particles…
In this work we study scalar products of Bethe vectors associated with the $XXZ$ spin chain with open boundary conditions. The scalar products are obtained as solutions of a system of functional equations. The description of scalar products…
The spectral problem of the Heisenberg XXZ spin-$\frac{1}{2}$ chain on the segment is investigated within a modified algebraic Bethe ansatz framework. We consider in this work the most general boundaries allowed by integrability. The…
The modified algebraic Bethe ansatz, introduced by Cramp\'e and the author [8], is used to characterize the spectral problem of the Heisenberg XXZ spin-$\frac{1}{2}$ chain on the segment with lower and upper triangular boundaries. The…
The spectral properties of operators formed from generators of the q-Onsager non-Abelian infinite dimensional algebra are investigated. Using a suitable functional representation, all eigenfunctions are shown to obey a second-order…
We consider closed XXX spin chains with broken total spin $U(1)$ symmetry within the framework of the modified algebraic Bethe ansatz. We study multiple actions of the modified monodromy matrix entries on the modified Bethe vectors. The…
We consider XXX spin-$1/2$ Heisenberg chain with non-diagonal boundary conditions. We obtain a compact determinant representation for the scalar product of on-shell and off-shell Bethe vectors. In the particular case when both Bethe vectors…
The Bethe ansatz, both in its coordinate and its algebraic version, is an exceptional method to compute the eigenvectors and eigenvalues of integrable systems. However, computing correlation functions using the eigenvectors thus constructed…
The anomalous dimensions of local single trace gauge invariant operators in N=4 supersymmetric Yang-Mills theory can be computed by diagonalizing a long range integrable Hamiltonian by means of perturbative asymptotic Bethe ansatz. This…
We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. We obtain a determinant representation for particular case of scalar products of Bethe vectors. This representation can be used for the calculation of…
We study the anomalous dimensions of operators in the scalar sector of \beta-deformed ABJ(M) theories. We show that the anomalous dimension matrix at two-loop order gives an integrable Hamiltonian acting on an alternating SU(4) spin chain…