Related papers: Algebraic construction of quantum integrable model…
A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an…
This thesis considers massive field theories in 1+1 dimensions known as affine Toda quantum field theories. We first consider the boundary sine-Gordon model, deriving a complete picture of the boundary bound state structure for general…
We define a new class of integrable vertex models associated to quantum groups at roots of unit
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
The standard generators of tridiagonal algebras, recently introduced by Terwilliger, are shown to generate a new (in)finite family of mutually commuting operators which extends the Dolan-Grady construction. The involution property relies on…
Basic notions regarding classical integrable systems are reviewed. An algebraic description of the classical integrable models together with the zero curvature condition description is presented. The classical r-matrix approach for discrete…
Basic concepts of quantum integrable systems (QIS) are presented stressing on the unifying structures underlying such diverse models. Variety of ultralocal and nonultralocal models is shown to be described by a few basic relations defining…
In this study, an integrable vertex model based on the quantum affine superalgebra $U_q\bigl(\hat{gl}(2|2)\bigr)$ is constructed. The model is characterized by a particular assignment of spectral parameters and lowest as well as highest…
Analog quantum simulation has the potential to be an indispensable technique in the investigation of complex quantum systems. In this work, we numerically investigate a one-dimensional, faithful, analog, quantum electronic circuit simulator…
We construct integrable spin chains with inhomogeneous periodic disposition of the anisotropy parameter. The periodicity holds for both auxiliary (space) and quantum (time) directions. The integrability of the model is based on a set of…
A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the…
The present thesis deals with some properties of classical and quantum scalar fields in an inhomogeneous and/or time-dependent background, focusing on models where the latter can be described as a curved space-time with an event horizon.…
Mathematical models of quantum computers such as a multidimensional quantum Turing machine and quantum circuits are described and its relations with lattice spin models are discussed. One of the main open problems one has to solve if one…
If we start from certain functional relations as definition of a quantum integrable theory, then we can derive from them a linear integral equation. It can be extended, by introducing dynamical variables, to become an equation with the form…
Various applications of quantum algebraic techniques in nuclear structure physics, such as the su$_q$(2) rotator model and its extensions, the use of deformed bosons in the description of pairing correlations, and the construction of…
In this paper, we develop the framework for quantum integrable systems on an integrable classical background. We call them hybrid quantum integrable systems (hybrid integrable systems), and we show that they occur naturally in the…
To a given algebraic curve we assign an infinite family of quantum curves (Schr\"odinger equations), which are in one-to-one correspondence with, and have the structure of, Virasoro singular vectors. For a spectral curve of a matrix model…
We propose a regular way to construct lattice versions of $W$-algebras, both for quantum and classical cases. In the classical case we write the algebra explicitly and derive the lattice analogue of Boussinesq equation from the Hamiltonian…
The first part of this paper explains what super-integrability is and how it differs in the classical and quantum cases. This is illustrated with an elementary example of the resonant harmonic oscillator. For Hamiltonians in "natural form",…
With appropriate boundary conditions the anisotropic $XY$ chain in a magnetic field is known to be invariant under quantum group transformations. We generalize this model defining a class of integrable chains with several fermionic degrees…