Related papers: Boundary transfer matrices arising from quantum sy…
The isotropic XY model $(s=1/2)$ in a transverse field, with uniform long-range interactions among the transverse components of the spins, on the inhomogeneous periodic chain, is studied. The model, composed of $N$ segments with $n$…
We elaborate on the proposed general boundary formulation as an extension of standard quantum mechanics to arbitrary (or no) backgrounds. Temporal transition amplitudes are generalized to amplitudes for arbitrary spacetime regions. State…
In this survey, we review some of the recent connections between the representation theory of (untwisted) quantum affine algebras and the representation theory of current algebras. We mainly focus on the finite-dimensional representations…
We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are…
We develop a transfer-matrix formulation of the scattering of electromagnetic waves by a general isotropic medium which makes use of a notion of electromagnetic transfer matrix $\mathbf{M}$ that does not involve slicing of the scattering…
We continue our exercises with the universal $R$-matrix based on the Khoroshkin and Tolstoy formula. Here we present our results for the case of the twisted affine Kac--Moody Lie algebra of type $A^{(2)}_2$. Our interest in this case is…
The half-infinite XXZ open spin chain with general integrable boundary conditions is considered within the recently developed `Onsager's approach'. Inspired by the finite size case, for any type of integrable boundary conditions it is shown…
In this paper, we present an algorithm for computing a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in several variables. This algorithm is a generalization of a method developed for…
We show that the set of transfer matrices of an arbitrary fusion type for an integrable quantum model obey these bilinear functional relations, which are identified with an integrable dynamical system on a Grassmann manifold (higher Hirota…
For the classical principal chiral model with boundary, we give the subset of the Yangian charges which remains conserved under certain integrable boundary conditions, and extract them from the monodromy matrix. Quantized versions of these…
In this paper we apply our new separation of variables approach to completely characterize the transfer matrix spectrum for quantum integrable lattice models associated to fundamental evaluation representations of $\mathcal{U}_{q}…
Here we study the problem of generalizing one of the main tools of Groebner basis theory, namely the flat deformation to the leading term ideal, to the border basis setting. After showing that the straightforward approach based on the…
Affine Toda field theories with a purely transmitting integrable defect are considered and the model based on a_2 is analysed in detail. After providing a complete characterization of the problem in a classical framework, a suitable quantum…
We consider the quantum inverse scattering method for several mixed integrable models based on the rational SU(N) R-matrix with general toroidal boundary conditions. This includes systems whose Hilbert spaces are invariant by the discrete…
We diagonalize infinitely many commuting operators $T_B(z)$. We call these operators $T_B(z)$ the boundary transfer matrix associated with the quantum group and the elliptic quantum group. The boundary transfer matrix is related to the…
This work concerns the boundary integrability of the spin-s ${\cal{U}}_{q}[sl(2)]$ Temperley-Lieb model. A systematic computation method is used to constructed the solutions of the boundary Yang-Baxter equations. For $s$ half-integer, a…
We diagonalise the transfer matrix of boundary ABF models using bosonized vertex operators. We compute the boundary S-matrix and check the scaling limit against known results for perturbed boundary conformal field theories.
We develop crossing symmetric dispersion relations for describing 2-2 scattering of identical external particles carrying spin. This enables us to import techniques from Geometric Function Theory and study two sided bounds on low energy…
A class of models is considered for a quantum particle constrained on degenerate Riemannian manifolds known as Grushin cylinders, and moving freely subject only to the underlying geometry: the corresponding spectral analysis is developed in…
We study the boundary S-matrix for the reflection of bound states of the two-dimensional sine-Gordon integrable field theory in the presence of a boundary.