Related papers: Lattice models, differential forms, and the Yang-B…
We propose a fully discrete analog of the massive Thirring model in light-cone coordinates by constructing its Lax-pair representation. This Lax-pair representation can also be used to define a new Yang-Baxter map, so we obtain a…
We show that the Yang-Baxter equations for two dimensional models admit as a group of symmetry the infinite discrete group $A_2^{(1)}$. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the…
In this paper we investigate the mathematical properties of the integrability of the symmetric six-vertex model towards the view of Algebraic Geometry. We show that the algebraic variety originated from Baxter's commuting transfer method is…
We construct integrable boundary conditions for sl(2) coset models with central charges c=3/2-12/(m(m+2)) and m=3,4,... The associated cylinder partition functions are generating functions for the branching functions but these boundary…
We extend our recent work on set-theoretic solutions of the Yang-Baxter or braid relations with new results about their automorphism groups, strong twisted unions of solutions and multipermutation solutions. We introduce and study graphs of…
In p-form lattice gauge theory, the fluctuating variables live on p-dimensional cells and interact around (p+1)-dimensional cells. It has been argued that the continuum version of this model should be described by (p-1)-gerbes. However,…
The deformed algebra $\cal{A(R)}$, depending upon a Yang-Baxter R- matrix, is considered. The conditions under which the algebra is associative are discussed for a general number of oscillators. Four types of solutions satisfying these…
Nine classes of integrable boundary conditions for the eight-state supersymmetric model of strongly correlated fermions are presented. The boundary systems are solved by using the coordinate Bethe ansatz method and the Bethe ansatz…
We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These…
In this article, a system of Yang-Baxter-type matrix equations is studied, $XAX=BXB$, $XBX=AXA$, which "generalizes" the matrix Yang-Baxter equation and exhibits a broken symmetry. We investigate the solutions of this system from various…
We discuss some of the difficulties that have been mentioned in the literature in connection with the Bethe ansatz for the six-vertex model and XXZ chain, and for the eight-vertex model. In particular we discuss the ``beyond the equator'',…
Exotic states have been predicted before and after the advent of QCD. In the last decades they have been observed at accelerator experiments in the sector with two heavy quarks, at or above the quarkonium strong decay threshold and called X…
We consider a hierarchy of many particle systems on the line with polynomial potentials separable in parabolic coordinates. Using the Lax representation, written in terms of $2\times 2$ matrices for the whole hierarchy, we construct the…
In order to make graphical Gaussian models a viable modelling tool when the number of variables outgrows the number of observations, model classes which place equality restrictions on concentrations or partial correlations have previously…
We introduce "noninvertible" generalization of statistics - semistatistics replacing condition when double exchanging gives identity to "regularity" condition. Then in categorical language we correspondingly generalize braidings and the…
We study involutive set-theoretic solutions of the Yang-Baxter equation of multipermutation level 2. These solutions happen to fall into two classes -- distributive ones and non-distributive ones. The distributive ones can be effectively…
We consider a rational six vertex model on a rectangular lattice with boundary conditions that generalize the usual domain wall type. We find that the partition function of the inhomogeneous version of this model is given by a modified…
This note gives a general construction of an integrable lattice model (and a solution of the Yang-Baxter equation with spectral parameter) from a four-dimensional field theory which is a mixture of topological and holomorphic. Spin-chain…
Grid states form a discrete set of mixed quantum states that can be described by graphs. We characterize the entanglement properties of these states and provide methods to evaluate entanglement criteria for grid states in a graphical way.…
We introduce the notion of ortho-symplectic super triple system, and apply it to find solutions of super Yang-Baxter equation. Also, the para-statistics are formulated as a Lie-super triple system.