Related papers: Integrability of planar-algebraic models
The numerical algorithm of the inverse quantum scattering is developed. This algorithm is based on the Marchenko theory, and includes three steps. The first one is the algebraic Pade approximation of the unitary S-matrix, what is realized…
We develop a unified formulation of the quantum inverse scattering method for lattice vertex models associated to the non-exceptional $A^{(2)}_{2r}$, $A^{(2)}_{2r-1}$, $B^{(1)}_r$, $C^{(1)}_r$, $D^{(1)}_{r+1}$ and $D^{(2)}_{r+1}$ Lie…
We propose the full system of Baxter Q-functions (QQ-system) for the integrable spin chains with the symmetry of the $D_r$ Lie algebra. We use this QQ-system to derive new Weyl-type formulas expressing transfer matrices in all symmetric and…
In this short proceedings we discuss some of the results obtained in [1]. Integrable deformations enlarge the landscape and understanding of integrable models and its algebraic structures like quantum groups. In this short proceedings, we…
The main purpose of this paper is to introduce a new class of Hamiltonian scattering systems of the cone potential type that can be integrated via the asymptotic velocity. For a large subclass, the asymptotic data of the trajectories define…
On the basis of the explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices, we derive a new representation for the…
Quadratic systems generated using Yang-Baxter equations are integrable in a sense, but we display a deterioration in the possession of the Painlev\'e property as the number of equations in each `integrable system' increases. Certain…
We show that integrability of the BCS model extends beyond Richardson's model (where all Cooper pair scatterings have equal coupling) to that of the russian doll BCS model for which the couplings have a particular phase dependence that…
A new hidden symmetry is exhibited in the reflection equation and related quantum integrable models. It is generated by a dual pair of operators $\{\textsf{A}, \textsf{A}^*\}\in{\cal A}$ subject to $q-$deformed Dolan-Grady relations. Using…
We implement the quantum inverse scattering method for the 4-vertex model. In comparison to previous works of the author which examined the 6-vertex, and 20-vertex, models, the 4-vertex model exhibits different characteristics, ranging from…
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…
We investigate the inverse scattering problem for the massive Thirring model, focusing particularly on cases where the transmission coefficient exhibits $N$ pairs of higher-order poles. Our methodology involves transforming initial data…
A special case of the Fateev-Zamolodchikov model is studied resulting in a solution of the Yang-Baxter equation with two spectral parameters. Integrable models from this solution are shown to have the symmetry of the Drinfeld double of a…
The integrability of the one-dimensional (1D) fermion chain model is investigated in the framework of the Quantum Inverse Scattering Method (QISM). We introduce a new R-operator for the fermion chain model, which is expressed in terms of…
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using…
A non-unitary version of quantum scattering is studied via an exactly solvable toy model. The model is merely asymptotically local since the smooth path of the coordinate is admitted complex in the non-asymptotic domain. At any real…
An extension of the supersymmetric U model for correlated elctrons is given and integrability is established by demonstrating that the model can be constructed through the Quantum Inverse Scattering Method using an R-matrix without the…
The dimer model on a strip is considered as a Yang-Baxter \mbox{integrable} six vertex model at the free-fermion point with crossing parameter $\lambda=\tfrac{\pi}{2}$ and quantum group invariant boundary conditions. A one-to-many mapping…
The path integral of a quantum system with an exact symmetry can be written as a sum of functional integrals each giving the contribution from quantum states with definite symmetry properties. We propose a strategy to compute each of them,…
Based on the (quantum) twisted Yangians, integrable systems with special boundary conditions, called soliton non-preserving (SNP), may be constructed. In the present article we focus on the study of subalgebras of the (quantum) twisted…