Related papers: Bethe Equations "on the Wrong Side of Equator"
A new exactly solvable one-dimensional spin-3/2 Heisenberg model with SO(5)-invariance is proposed. The eigenvalues and Bethe ansatz equations of the model are obtained by using the nested algebraic Bethe ansatz approach. Several exotic…
We find an analytic solution of the Bethe Ansatz equations (BAE) for the special case of a finite XXZ spin chain with free boundary conditions and with a complex surface field which provides for $U_q(sl(2))$ symmetry of the Hamiltonian.…
We study properties of transfer matrices in the sl(N) spin chain models. The transfer matrices with an infinite dimensional auxiliary space are factorized into the product of N commuting Baxter Q-operators. We consider the transfer matrices…
We prove, using the coordinate Bethe ansatz, the exact solvability of a model of three particles whose point-like interactions are determined by the root system of g_2. The statistics of the wavefunction are left unspecified. Using the…
By using algebraic Bethe ansatz method, we give the Hamitonian of the spin-1 XXX chain associated with $sl_2$ with two boundary impurities.
In this proceeding we present the nested Bethe ansatz for open spin chains of XXX-type, with arbitrary representations (i.e. `spins') on each site of the chain and diagonal boundary matrices $(K^+(u),K^-(u))$. The nested Bethe anstaz…
Solutions to the twisted Yang-Baxter equation, arising from intertwiners for cyclic representations of $U_q(\widehat{sl}_n)$ are described via two coupled the lattice current algebras.
We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains.…
The quantum $\tau_2$-model with generic site-dependent inhomogeneity and arbitrary boundary fields is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix are given in terms of an…
The rational $Q$-system is an efficient method to solve Bethe ansatz equations for quantum integrable spin chains. We construct the rational $Q$-systems for generic Bethe ansatz equations described by an $A_{\ell-1}$ quiver, which include…
Establishing the completeness of a Bethe Ansatz solution for an exactly solved model is a perennial challenge, which is typically approached on a case by case basis. For the rational, spin-1/2 Richardson--Gaudin system it will be argued…
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…
We express $D^{(2)}_{2}$ transfer matrices as products of $A^{(1)}_{1}$ transfer matrices, for both closed and open spin chains. We use these relations, which we call factorization identities, to solve the models by algebraic Bethe ansatz.…
The three different sets of Bethe ansatz equations describing the Bethe ansatz solution of the supersymmetric t-J model are known to be equivalent. Here we give a new, simplified proof of this fact which relies on the properties of certain…
The eigenvectors of the Hamiltonian ${\cal H}_{N}$ of $N$-sites quantum spin chains with elliptic exchange are connected with the double Bloch meromorphic solutions of the quantum continuous elliptic Calogero-Moser problem. This fact allows…
We have recently proposed a Bethe Ansatz solution of the open spin-1/2 XXZ quantum spin chain with general integrable boundary terms (containing six free boundary parameters) at roots of unity. We use this solution, together with an…
We discuss the construction of Baxter's Q-operator. The suggested approach leads to the one-parametric family of Q-operators, satisfying to the wronslian-type relations. Also we have found the generalization of Baxter operators, with…
Changing the variables in the Bethe Ansatz Equations (BAE) for the XXZ six-vertex model we had obtained a coupled system of polynomial equations. This provided a direct link between the BAE deduced from the Algebraic Bethe Ansatz (ABA) and…
We consider the open XXZ quantum spin chain with nondiagonal boundary terms. For bulk anisotropy value \eta = i \pi/(p+1), p= 1, 2, ..., we propose an exact (p+1)-order functional relation for the transfer matrix, which implies…
A quantum integrable spin chain model associated with the $G_2$ exceptional Lie algebra is studied. By using the fusion technique, the closed recursive relations among the fused transfer matrices are obtained. These identities allow us to…