相关论文: New Q matrices and their functional equations for …
The set of forks is a class of quivers introduced by M. Warkentin, where every connected mutation-infinite quiver is mutation equivalent to infinitely many forks. Let $Q$ be a fork with $n$ vertices, and $\boldsymbol{w}$ be a…
We study the solutions of the Yang-Baxter equation associated to nineteen vertex models invariant by the parity-time symmetry from the perspective of algebraic geometry. We determine the form of the algebraic curves constraining the…
The solution of Bethe ansatz equations for XXZ spin chain with the parameter $q$ being a root of unity is infamously subtle. In this work, we develop the rational $Q$-system for this case, which offers a systematic way to find all physical…
Many well-known and well-studied four by four universal quantum logic gates in the literature are of a specific form, the so called eight-vertex form \eqref{8vertexform} \cite{kaufman etal 05-1,kaufman etal 05-2}, or {\it similar} to it. We…
In this paper we review the theory of the Yang-Baxter equation related to the 6-vertex model and its higher spin generalizations. We employ a 3D approach to the problem. Starting with the 3D R-matrix, we consider a two-layer projection of…
New solutions of the quantum Yang-Baxter equation, depending in general on three arbitrary parameters, are written down. They are based on the root of unity representations of the quantum orthosymplectic superalgebra \\U, which were found…
We consider two new families of quantum vertex algebras which are associated with the type $A$ trigonometric $R$-matrix and elliptic $R$-matrix of the eight-vertex model. We show that their $\phi$-coordinated representation theory is…
We demonstrate that the transfer matrix of the inhomogeneous $N$-state chiral Potts model with two vertical superintegrable rapidities serves as the $Q$-operator of XXZ chain model for a cyclic representation of $U_{\sf q}(sl_2)$ with $N$th…
We provide two methods of producing the $Q$-operator of XXZ spin chain of higher spin, one for $N$th root-of-unity $q$ with odd $N$ and another for a general $q$, as the generalization of those known in the six-vertex model. In the…
In this paper, we construct a Q-operator as a trace of a representation of the universal R-matrix of $U_q(\hat{sl}_2)$ over an infinite-dimensional auxiliary space. This auxiliary space is a four-parameter generalization of the q-oscillator…
We study a natural q-analogue of a class of matrices with noncommutative entries, which were first considered by Yu. I. Manin in 1988 in relation with quantum group theory, (called Manin Matrices in [5]) . These matrices we shall call…
It is shown that for a certain class of Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) the Lax representation can be derived straight from the map itself. A similar phenomenon for 3D consistent equations…
We show that the action of universal $R$-matrix of affine $U_qsl_2$ quantum algebra, when $q$ is a root of unity, can be renormalized by some scalar factor to give a well defined nonsingular expression, satisfying Yang-Baxter equation. It…
The spin-1/2 Heisenberg XXZ chain is a paradigmatic quantum integrable model. Although it can be solved exactly via Bethe ansatz techniques, there are still open issues regarding the spectrum at root of unity values of the anisotropy. We…
We formulate and discuss two conjectures concerning recursive formulae for Branson's $Q$-curvatures. The proposed formulae describe all $Q$-curvatures on manifolds of all even dimensions in terms of respective lower order $Q$-curvatures and…
We consider integrable vertex models whose Boltzmann weights (R-matrices) are trigonometric solutions to the graded Yang-Baxter equation. As is well known the latter can be generically constructed from quantum affine superalgebras…
The q-characters were introduced by Frenkel and mReshetikhin to study finite dimensional representations of the untwisted quantum affine algebra for q generic. The $\epsilon$-characters at roots of unity were constructed by Frenkel and…
Baxter's Q-operator is generally believed to be the most powerful tool for the exact diagonalization of integrable models. Curiously, it has hitherto not yet been properly constructed in the simplest such system, the compact spin-1/2…
We find the all solutions to the $sl_q(2)$-invariant multi-parametric Yang-Baxter equations (YBE) at $q=i$ defined on the cyclic (semi-cyclic, nilpotent) representations of the algebra. We are deriving the solutions in form of the linear…
We obtain the Baxter Q-operators in the $U_q(\hat{sl}_2)$ invariant integrable models as a special limits of the quantum transfer matrices corresponding to different spins in the auxiliary space both from the functional relations and from…