Related papers: Separation of variables for rational gl(n) spin ch…
We propose a basis for rational gl(N) spin chains in an arbitrary rectangular representation $(S^A)$ that factorises the Bethe vectors into products of Slater determinants in Baxter Q-functions. This basis is constructed by repeated action…
Based on the method of separation of variables due to Sklyanin, we construct a new integral representation for the scalar products of the Bethe states for the SU(2) XXX spin 1/2 chain obeying the periodic boundary condition. Due to the…
We conjecture a new way to construct eigenstates of integrable XXX quantum spin chains with SU(N) symmetry. The states are built by repeatedly acting on the vacuum with a single operator Bgood(u) evaluated at the Bethe roots. Our proposal…
The antiperiodic transfer matrix associated to higher spin representations of the rational 6-vertex Yang-Baxter algebra is analyzed by generalizing the approach introduced recently in [1], for the cyclic representations, in [2], for the…
We formulate the functional Bethe ansatz for bosonic (infinite dimensional) representations of the Yang-Baxter algebra. The main deviation from the standard approach consists in a half infinite 'Sklyanin lattice' made of the eigenvalues of…
Following Sklyanin's proposal in the periodic case, we derive the generating function of the Gaudin Hamiltonians with boundary terms. Our derivation is based on the quasi-classical expansion of the linear combination of the transfer matrix…
We apply the Sklyanin method of separation of variables to the reflection algebra underlying the open spin-1/2 XXX chain with non-diagonal boundary fields. The spectral problem can be formulated in terms of a TQ-equation which leads to the…
We consider the N-site U_{q}(gl(N)) integrable spin chain with periodic and open diagonal soliton-preserving boundary conditions. By employing analytical Bethe ansatz techniques we are able to determine the spectrum and the corresponding…
Integrable sl(N) spin chains, which we consider in this paper, are not only the prototypical example of quantum integrable systems but also systems with a wide range of applications. For these models we use the Functional Separation of…
The Functional Bethe Ansatz (FBA) proposed by Sklyanin is a method which gives separation variables for systems for which an $R$-matrix is known. Previously the FBA was only known for $SL(2)$ and $SL(3)$ (and associated) $R$-matrices. In…
In the derivation of the generating function of the Gaudin Hamiltonians with boundary terms, we follow the same approach used previously in the rational case, which in turn was based on Sklyanin's method in the periodic case. Our derivation…
We present an "algebraic treatment" of the analytical Bethe Ansatz. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe Ansatz. It allows us to deal with a…
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)…
In this paper we take further steps towards developing the separation of variables program for integrable spin chains with gl(N) symmetry. By finding, for the first time, the matrix elements of the SoV measure explicitly we were able to…
In this note we propose an approach for a fast analytic determination of all possible eigenstates of rational GL(N|M) integrable spin chains of given not too large length, in terms of Baxter Q-functions. We observe that all exceptional…
We describe the extension, beyond fundamental representations of the Yang-Baxter algebra, of our new construction of separation of variables bases for quantum integrable lattice models. The key idea underlying our approach is to use the…
We propose a non-standard separation of variables for the classical integrable XXX and XXZ spin chains with degenerate twist matrix. We show that for the case of such twist matrices one can interchange the role of classical separating…
We construct the Baxter Q-operator and the representation of the Separated Variables (SoV) for the homogeneous open SL(2,R) spin chain. Applying the diagrammatical approach, we calculate Sklyanin's integration measure in the separated…
We present a new approach to construct the separate variables basis leading to the full characterization of the transfer matrix spectrum of quantum integrable lattice models. The basis is generated by the repeated action of the transfer…
We present an ``algebraic treatment'' of the analytical Bethe ansatz for open spin chains with soliton non preserving (SNP) boundary conditions. For this purpose, we introduce abstract monodromy and transfer matrices which provide an…