Related papers: On different approaches to integrable lattice mode…
We extend basic properties of two dimensional integrable models within the Algebraic Bethe Ansatz approach to 2+1 dimensions and formulate the sufficient conditions for the commutativity of transfer matrices of different spectral…
Quantum universal enveloping algebras, quantum elliptic algebras and double (deformed) Yangians provide fundamental algebraic structures relevant for many integrable systems. They are described in the FRT formalism by R-matrices which are…
We consider a class of models of non-equilibrium electronic Mach-Zehnder interferometers built on integer quantum Hall edges states. The models are characterized by the electron-electron interaction being restricted to the inner part of the…
By defining a graded global R-operator $\mathbb{R}_{ab}^{(2D,2S)}$ that couples free-fermion structures and incorporates anisotropic Hubbard interactions while satisfying the Yang--Baxter equation, we construct a strictly solvable…
We study a crack lying along an imperfect interface in an anisotropic bimaterial. A method is devised where known weight functions for the perfect interface problem are used to obtain singular integral equations relating the tractions and…
A systematic study for a single-specie lattice Boltzmann model with frustrated-short range attractive and mid/long-range repulsive-interactions is presented. The equilibrium analysis is performed along the guidelines proposed by [X. Shan,…
We study numerically the ODE/IM correspondence for untwisted affine Lie algebras associated with simple Lie algebras including exceptional type. We consider the linear problem obtained from the massless limit of that of the modified affine…
We initiate a new study on the correspondence between the 20-vertex model and a SOS (Solid-on-Solid) model. In comparison to two previous works of the author in 2024 which characterized properties of the transfer, and quantum monodromy,…
We consider the logarithmic minimal models LM(1,p) as `rational' logarithmic conformal field theories with extended W symmetry. To make contact with the extended picture starting from the lattice, we identify 4p-2 boundary conditions as…
This document reports investigations of models of multiphase flows using Lattice Boltzmann methods. The emphasis is on deriving by Chapman-Enskog techniques the corresponding macroscopic equations. The singular interface…
We use the reduced relaxed micromorphic model (RRMM) to capture the effective "bulk" dynamical response of finite size metamaterial specimens made out of a Labyrinthine unit cell. We show that for small finite-size specimens, boundary…
Two dimensional statistical integrable models, such as the Ising model, the chiral Potts model and the Belavin model, becomes integrable. Because of the SU(2) symmetry of these models, these models become integrable. The integral models are…
In this paper we investigate a correspondence among spin and vertex models with the same number of local states on the square lattice with toroidal boundary conditions. We argue that the partition functions of an arbitrary $n$-state spin…
We study a quantum Yang-Baxter structure associated with non-ultralocal lattice models. We discuss the canonical structure of a class of integrable quantum mappings, i.e. canonical transformations preserving the basic commutation relations.…
Conformal blocks for the WZW model on tori can be represented by vector valued Weyl anti-symmetric theta functions on the Cartan subalgebra satisfying vanishing conditions on root hyperplanes. We introduce a quantum version of these…
We introduce the notion of the ell-weight lattice and the ell-root lattice adapted to the study of finite-dimensional representations of quantum affine algebras. We then study the ell-weights of the fundamental representations and show that…
We study the Hopf algebra structure and the highest weight representation of a multiparameter version of $U_{q}gl(2)$. The commutation relations as well as other Hopf algebra maps are explicitly given. We show that the multiparameter…
We consider the integrable XXZ model with the special open boundary conditions. We perform Quantum Group reduction of this model in roots of unity and use it for the definition Minimal Models of Interable lattice theory. It is shown that…
Applying braided Yang-Baxter equation quantum integrable and Bethe ansatz solvable 1D anyonic lattice and field models are constructed. Along with known models we discover novel lattice anyonic and $q$-anyonic models as well as nonlinear…
We present a fully-integrated lattice Boltzmann (LB) method for fluid--structure interaction (FSI) simulations that efficiently models deformable solids in complex suspensions and active systems. Our Eulerian method (LBRMT) couples…