Related papers: Singular solutions, repeated roots and completenes…
We consider the Bethe equations for the isotropic spin-1/2 Heisenberg quantum spin chain with periodic boundary conditions. We formulate a conjecture for the number of solutions with pairwise distinct roots of these equations, in terms of…
The Bethe equations for the isotropic periodic spin-1/2 Heisenberg chain with N sites have solutions containing i/2, -i/2 that are singular: both the corresponding energy and the algebraic Bethe ansatz vector are divergent. Such solutions…
Bethe ansatz equations for spin-$s$ Heisenberg spin chain with $s\ge1$ are significantly more difficult to analyze than the spin-$\tfrac{1}{2}$ case, due to the presence of repeated roots. As a result, it is challenging to derive extra…
The Bethe equations for the periodic XXX and XXZ spin chains admit singular solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions…
We study the implications of the regularization for the singular solutions on the even(odd) length spin-1/2 XXX chains in some specific down-spin sectors. In particular, the analytic expressions of the Bethe eigenstates for three down-spin…
In integrable spin chains, the spectral problem can be solved by the method of Bethe ansatz, which transforms the problem of diagonalization of the Hamiltonian into the problem of solving a set of algebraic equations named Bethe equations.…
We observe a different type of complex solutions in the isotropic spin-1/2 Heisenberg chain starting from N=12, where the central rapidity of some of the odd-length strings becomes complex making not all the strings self-conjugate…
The exact solution of an integrable anisotropic Heisenberg spin chain with nearest-neighbour, next-nearest-neighbour and scalar chirality couplings is studied, where the boundary condition is the antiperiodic one. The detailed construction…
We provide a conjecture for the following two quantities related with the spin-$\frac{1}{2}$ isotropic Heisenberg model defined over rings of even lengths: (i) the number of the solutions to the Bethe ansatz equations which correspond to…
The properties of the most probable ground state candidate for the XXZ spin chain with the anisotropy parameter equal to -1/2 and an odd number of sites is considered. Some linear combinations of the components of the considered state,…
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 derive exactly the number of complex solutions with two down-spins in the massive regime of the periodic spin-1/2 XXZ spin chain of $N$ sites. Here we remark that every solution of the Bethe ansatz equations is characterized by a set of…
We consider the open spin-s XXZ quantum spin chain with N sites and general integrable boundary terms for generic values of the bulk anisotropy parameter, and for values of the boundary parameters which satisfy a certain constraint. We…
Every solution of the Bethe-ansatz equations (BAE) is characterized by a set of quantum numbers, by which we can evaluate it numerically. However, no general rule is known how to give quantum numbers for the physical solutions of BAE. For…
In this paper we investigate complex solutions of the Bethe equations in the two-particle sector both for arbitrary finite number of sites and for the thermodynamic limit . We find the number of complex solutions (strings) and compare it…
We propose a method to determine the quantum numbers, which we call the rigged configurations, for the solutions to the Bethe ansatz equations for the spin-1/2 isotropic Heisenberg model under the periodic boundary condition. Our method is…
The full set of polynomial solutions of the nested Bethe Ansatz is constructed for the case of A_2 rational spin chain. The structure and properties of these associated solutions are more various then in the case of usual XXX (A_1) spin…
In this paper we count the numbers of real and complex solutions to Bethe constraints in the two particle sector of the XXZ model. We find exact number of exceptions to the string conjecture and total number of solutions which is required…
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)…
We examine the question of whether Bethe's ansatz reproduces all states in the periodic Heisenberg XXZ and XXX spin chains. As was known to Bethe himself, there are states for which the Bethe momenta $k_n$ diverge: these are in fact the…