Related papers: SOV approach for integrable quantum models associa…
We develop a method for computing form factors of local operators in the framework of Sklyanin's separation of variables (SOV) approach to quantum integrable systems. For that purpose, we consider the sine-Gordon model on a finite lattice…
Separation of variables by means of the orbit method is implemented to integrable systems on coadjoint orbits in an $\mathfrak{sl}(4)$ loop algebra. This is a development and a kind of explanation for Sklyanin's procedure of separation of…
In this paper we continue our derivation of the correlation functions of open quantum spin 1/2 chains with unparallel magnetic fields on the edges; this time for the more involved case of the XXZ spin 1/2 chains. We develop our study in the…
The major simplification in a number of quantum integrable systems is the existence of special coordinates in which the eigenstates take a factorised form. Despite many years of studies, the basis realising the separation of variables (SoV)…
In this first paper, we start the analysis of correlation functions of quantum spin chains with general integrable boundary conditions. We initiate these computations for the open XXX spin 1/2 quantum chains with some unparallel magnetic…
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…
An orthogonal basis of the Hilbert space for the quantum spin chain associated with the su(3) algebra is introduced. Such kind of basis could be treated as a nested generalization of separation of variables (SoV) basis for high-rank quantum…
We introduce a universal framework for boundary transfer matrices, inspired by Sklyanin's two-row transfer matrix approach for quantum integrable systems with boundary conditions. The main examples arise from quantum symmetric pairs of…
This study presents fast and accurate analytical methods for transient thermal modeling in multi-layer composites with an arbitrary number of layers. The proposed approach accounts for internal heat generation and non-homogeneities in the…
The procedure for obtaining integrable vertex models via reflection matrices on the square lattice with open boundaries is reviewed and explicitly carried out for a number of two- and three-state vertex models. These models include the…
The quantum separation of variables method consists in mapping the original Hilbert space where a spectral problem is formulated onto one where the spectral problem takes a simpler "separated" form. In order to realise such a program, one…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
We explain how to compute correlation functions at zero temperature within the framework of the quantum version of the Separation of Variables (SoV) in the case of a simple model: the XXX Heisenberg chain of spin 1/2 with twisted…
For a system of linear partial differential equations (LPDEs) we introduce an operator equation for auxiliary operators. These operators are used to construct a kernel of an integral transformation leading the LPDE to the separation of…
Recently, a new quantum model - two-dimensional generalization of the Scarf II - was completely solved analytically by SUSY method for the integer values of parameter. Now, the same integrable model, but with arbitrary values of parameter,…
Using the orbit method we attempt to reveal geometric and algebraic meaning of separation of variables for the integrable systems on coadjoint orbits in an $\mathfrak{sl}(3)$ loop algebra. We consider two types of generic orbits embedded…
In this paper, we consider the quantum XYZ open spin-1/2 chain with boundary fields. We focus on the particular case in which the six boundary parameters are related by a single constraint enabling us to describe part of the spectrum by…
We study the exact solution of quantum integrable system associated with the $A^{(2)}_3$ twist Lie algebra, where the boundary reflection matrices have non-diagonal elements thus the $U(1)$ symmetry is broken. With the help of the fusion…
In the present paper, using a modification of the method of vector fields $Z_i$ of the bi-Hamiltonian theory of separation of variables (SoV), we construct symmetric non-St\"ackel variable separation for three-dimensional extension of 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…