Related papers: Integrability as a consequence of discrete holomor…
This monograph, written for educational purposes, serves as an introduction to the concept of integrability as it applies to systems of differential equations (both ordinary and partial) as well as to vector-valued fields. The general cases…
A method is introduced for constructing lattice discretizations of large classes of integrable quantum field theories. The method proceeds in two steps: The quantum algebraic structure underlying the integrability of the model is determined…
Using dynamical-mean-field theory for clusters, we study the two-dimensional Hubbard model in which electrons are coupled with the orthorhombic lattice distortions through the modulation in the hopping matrix. Instability towards…
An operator deformed quantum algebra is discovered exploiting the quantum Yang-Baxter equation with trigonometric R-matrix. This novel Hopf algebra along with its $q \to 1$ limit appear to be the most general Yang-Baxter algebra underlying…
We investigate the complexity of the partial order relation of Young's lattice. The definable relations are characterized by establishing the maximal definability property modulo the single automorphism given by conjugation; consequently,…
The discrete non-linear Schrodinger (NLS) model in the presence of an integrable defect is examined. The problem is viewed from a purely algebraic point of view, starting from the fundamental algebraic relations that rule the model. The…
A phenomenological model with itinerant bands and local states trapped by the lattice on the Cu-sites, is discussed to describe global features of cuprates. Relative energy positions of localized and itinerant states being tuned…
This article considers the relation between the spanning properties of lattice orbits of discrete series representations and the associated lattice co-volume. The focus is on the density theorem, which provides a trichotomy characterizing…
We investigate a Kondo lattice model with correlated conduction electrons. Within dynamical mean-field theory the model maps onto an impurity model where the host has to be determined self-consistently. This impurity model can be derived…
The work contains a detailed study of the scaling limit of a certain critical, integrable inhomogeneous six-vertex model subject to twisted boundary conditions. It is based on a numerical analysis of the Bethe ansatz equations as well as…
Integrable discrete scalar equations defined on a~two or a three dimensional lattice can be rewritten as difference systems in bond variables or in face variables respectively. Both the difference systems in bond variables and the…
We examine the modulational and parametric instabilities arising in a non-autonomous, discrete nonlinear Schr{\"o}dinger equation setting. The principal motivation for our study stems from the dynamics of Bose-Einstein condensates trapped…
The general framework for integrable discrete systems on R in particular containing lattice soliton systems and their q-deformed analogues is presented. The concept of regular grain structures on R, generated by discrete one-parameter…
Loop braid groups characterize the exchange of extended objects, namely loops, in three dimensional space generalizing the notion of braid groups that describe the exchange of point particles in two dimensional space. Their interest in…
We address the integrability conditions of the inverse problem of the calculus of variations for time-dependent SODE using the Spencer version of the Cartan-K\"ahler theorem. We consider a linear partial differential operator $P$ given by…
Yang-Baxter integrable dense $A_1^{(1)}$ and dilute $A_2^{(2)}$ loop models are considered on the torus in their simplest physical regimes. A combination of boundary conditions $(h,v)$ is applied in the horizontal and vertical directions…
By means of contact-density chain-growth simulations, we investigate a simple lattice model of a flexible polymer interacting with an attractive substrate. The contact density is a function of the numbers of monomer-substrate and…
Motivated by the correlated monopoles and vortices observed in lattice QCD, using Cho decomposition method and two successive gauge transformations which lead to the observation of configurations that include both monopoles and center…
In these notes evidence is presented for intepreting the moduli space of the integrable model associated to $N\!=\!2$ gauge theories with $N\!=\!4$ matter content, in terms of Calabi-Yau manifolds. We restrict to the case of gauge group…
The Gauge/YBE correspondence states a surprising connection between solutions to the Yang-Baxter equation with spectral parameters and partition functions of supersymmetric quiver gauge theories. This correspondence has lead to systematic…