Related papers: Some functional solutions of the Yang-Baxter equat…
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 consider a general anisotropic massive SU(N) fermionic model, and investigate its quantum integrability. In particular, by regularizing singular operator products, we derive a system of equations resulting in the S-matrix and find some…
Quantum groups were invented largely to provide solutions of the Yang-Baxter equation and hence solvable models in 2-dimensional statistical mechanics and one-dimensional quantum mechanics. They have been hugely successful. But not all…
We attach with every finite, involutive, nondegenerate set-theoretic solution of the Yang--Baxter equation a finite group that plays for the associated structure group the role that a finite Coxeter group plays for the associated…
Every unitary solution of the Yang-Baxter equation (R-matrix) in dimension $d$ can be viewed as a unitary element of the Cuntz algebra ${\mathcal O}_d$ and as such defines an endomorphism of ${\mathcal O}_d$. These Yang-Baxter endomorphisms…
We study involutive non-degenerate set-theoretic solutions (X,r) of the Yang-Baxter equation on a finite set X. The emphasis is on the case where (X,r) is indecomposable, so the associated permutation group acts transitively on X. One of…
We present a formula for an infinite number of universal quantum logic gates, which are $4$ by $4$ unitary solutions to the Yang-Baxter (Y-B) equation. We obtain this family from a certain representation of the cyclic group of order $n$. We…
We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite interval at zero density. $R$-matrix and monodromy matrix are obtained as limits from their known counterparts on the finite interval.…
A direct proof is given of the fact that the Cremmer-Gervais R-matrices satisfy the Yang-Baxter equation.
Tensor solutions ($r$-matrices) of the classical Yang-Baxter equation (CYBE) in a Lie algebra, obtained as the classical limit of the $R$-matrix solution of the quantum Yang-Baxter equation (QYBE), is an important structure appearing in…
A review of some recent results on the dynamical theory of the Yang-Baxter maps (also known as set-theoretical solutions to the quantum Yang-Baxter equation) is given. The central question is the integrability of the transfer dynamics. The…
In this note we straightforwardly derive and make use of the quantum R-matrix for the su(2|2) SYM spin-chain in the manifest su(1|2)-invariant formulation, which solves the standard quantum Yang-Baxter equation, in order to obtain the…
We use the fusion formulas of the symmetric group and of the Hecke algebra to construct solutions of the Yang-Baxter equation on irreducible representations of $\mathfrak{gl}_N$, $\mathfrak{gl}_{N|M}$, $U_q(\mathfrak{gl}_N)$ and…
We study a general ansatz for an odd supersymmetric version of the Kronecker elliptic function, which satisfies the genus one Fay identity. The obtained result is used for construction of the odd supersymmetric analogue for the classical…
Most of the set-theoretical solutions of the Yang-Baxter equation studied in the past years were non-degenerate multipermutation solutions. For degenerate solutions, a correct definition of multipermutation solutions has not been…
We establish a one-to-one correspondence between structure groups of non-degenerate, involutive and braided "set-theoretical" solutions of the quantum Yang-Baxter equation and Garside groups with a certain presentation. Moreover, we show…
We demonstrate that the left (and right) invariant Maurer-Cartan forms for any semi-simple Lie group enable one to construct solutions of the Yang-Mills equations on the group manifold equipped with the natural Cartan-Killing metric. For…
A new method for solving the Yang-Baxter equation is presented. It is based on the Taylor expansion of R-matrix which is developed up to the power lambda^6. Using this method the R-matrix for integrable spin ladder is calculated.
The new method of solving quantum mechanical problems is proposed. The finite, i.e. cut off, Hilbert space is algebraically implemented in the computer code with states represented by lists of variable length. Complete numerical solution of…
In the classification of solutions of the Yang--Baxter equation, there are solutions that are not deformations of the trivial solution (essentially the identity). We consider the algebras defined by these solutions, and the corresponding…