Related papers: Bethe ansatz and Isomonodromic deformations
Schlesinger transformations are discrete monodromy preserving symmetry transformations of the classical Schlesinger system. Generalizing well-known results from the Riemann sphere we construct these transformations for isomonodromic…
It has been known since the beginning of this century that isomonodromic problems --- typically the Painlev\'e transcendents --- in a suitable asymptotic region look like a kind of ``modulation'' of isospectral problem. This connection…
In this work, we generalize the numerical approach to Gaudin models developed earlier by us to degenerate systems showing that their treatment is surprisingly convenient from a numerical point of view. In fact, high degeneracies not only…
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…
Schlesinger transformations are algebraic transformations of a Fuchsian system that preserve its monodromy representation and act on the characteristic indices of the system by integral shifts. One of the important reasons to study such…
We introduce and study the dynamics of Chebyshev polynomials on $d>2$ real intervals. We define isoharmonic deformations as a natural generalization of the Chebyshev dynamics. This dynamics is associated with a novel class of constrained…
We derive thermodynamic Bethe ansatz equations describing the vacuum energy of the SU(2N)/Sp(N) nonlinear sigma model on a cylinder geometry. The starting points are the recently-proposed amplitudes for the scattering among the physical,…
We consider the problem of diagonalization of the hamiltonians of the Gaudin model, which is a quantum chain model associated to a simple Lie algebra. The hamiltonians of this model act on the tensor product of finite-dimensional…
We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. We obtain determinant representations for form factors of diagonal entries of the monodromy matrix. This representation can be used for the calculation of…
We solve the XXZ Gaudin model with generic boundary using the modified algebraic Bethe ansatz. The diagonal and triangular cases have been recovered in this general framework. We show that the model for odd or even lengths has two different…
We present a method to construct a basis of singular and non-singular common eigenvectors for Gaudin Hamiltonians in a tensor product module of the Lie algebra SL(2). The subset of singular vectors is completely described by analogy with…
We introduce higher order polynomial deformations of $A_1$ Lie algebra. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use the results to obtain exact (Bethe…
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…
We consider the action of the Bethe algebra B_K on (\otimes_{s=1}^k L_{\lambda^{(s)}})_\lambda, the weight subspace of weight $\lambda$ of the tensor product of k polynomial irreducible gl_N-modules with highest weights…
In these lecture notes, the representation theory of the Heisenberg group as well as Howe's construction of the metaplectic group by means of twisted convolution operators with generalized, complex Gaussians are reviewed, and it is shown…
The off-diagonal Bethe Ansatz method [1] is used to revisit the periodic XXX Heisenberg spin-1/2 chain. It is found that the spectrum of the transfer matrix can be characterized by an inhomogeneous T-Q relation, a natural but nontrivial…
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…
We formulate in terms of the quantum inverse scattering method the algebraic Bethe ansatz solution of the one-dimensional Hubbard model. The method developed is based on a new set of commutation relations which encodes a hidden symmetry of…
We study the trigonometric quantum spin-Calogero-Sutherland model, and the Haldane-Shastry spin chain as a special case, using a Bethe-ansatz analysis. We harness the model's Yangian symmetry to import the standard tools of integrability…
We diagonalize Q-operators for rational homogeneous sl(2)-invariant Heisenberg spin chains using the algebraic Bethe ansatz. After deriving the fundamental commutation relations relevant for this case from the Yang-Baxter equation we…