Related papers: Factorization of R-matrix and Baxter Q-operators f…
We present in a simple terms the theory of the factorizing operator introduced recently by Maillet and Sanches de Santos for the spin - 1/2 chains. We obtain the explicit expressions for the matrix elements of the factorizing operator in…
We generalize our recent explicit construction of the full hierarchy of Baxter Q-operators of compact spin chains with su(n) symmetry to the supersymmetric case su(n|m). The method is based on novel degenerate solutions of the graded…
We consider quantum spin chains arising from $N$-fold tensor products of the fundamental evaluation representations of $Y(sl_n)$ and $U_q(\hat{sl_n})$. Using the partial $F$-matrix formalism from the seminal work of Maillet and Sanchez de…
We propose that the Baxter's $Q$-operator for the XYZ quantum spin chain with open boundary conditions is given by the $j\to \infty$ limit of the corresponding transfer matrix with spin-$j$ (i.e., $(2j+1)$-dimensional) auxiliary space. The…
We survey the matrix product solutions of the Yang-Baxter equation obtained recently from the tetrahedron equation. They form a family of quantum $R$ matrices of generalized quantum groups interpolating the symmetric tensor representations…
Inspired by the integrable structures appearing in weakly coupled planar N=4 super Yang-Mills theory, we study Q-operators and Yangian invariants of rational integrable spin chains. We review the quantum inverse scattering method along with…
The Baxterization process for the dynamical Yang-Baxter equation is studied. We introduce the local dynamical Hecke ,Temperley-Lieb and Birman-Murakami-Wenzl operators, then by inserting spectral parameters, from each representation of…
We propose the operatorial form of Baxter's TQ-relations in a general form of the operatorial B\"acklund flow describing the nesting process for the inhomogeneous rational gl(K|M) quantum (super)spin chains with twisted periodic boundary…
Based on the conjecture for the exact eigenvalue of the transfer matrix of the higher half-integer spin XXZ chain at the Razumov-Stroganov point, we evaluate the corresponding Baxter's Q operator in closed form by solving the TQ equation.…
We present an uniform construction of the solution to the Yang- Baxter equation with the symmetry algebra $s\ell(2)$ and its deformations: the q-deformation and the elliptic deformation or Sklyanin algebra. The R-operator acting in the…
We study the rational solution of the Yang-Baxter equation with the supersymmetry algebra sl(2|1). The R-matrix acting in the tensor product of two arbitrary representations of the supersymmetry algebra can be represented as the product of…
For an arbitrary generalized quantum integrable spin chain we introduce a "master T -operator" which represents a generating function for commuting quantum transfer matrices constructed by means of the fusion procedure in the auxiliary…
Integrable sl(N) spin chains, which we consider in this paper, are not only the prototypical example of quantum integrable systems but also systems with a wide range of applications. For these models we use the Functional Separation of…
We diagonalize the $B$-element of monodromy matrix for noncompact open $SL(2,\mathbb{C})$ spin chain with boundary interaction. The monodromy matrix is defined in terms of $SL(2,\mathbb{C})$ $L$-operator and boundary $K$-matrix. The…
Using notation inherited from the six-vertex model, we construct diagrams that represent the action of the factorizing $F$-matrices associated to the finite length XXZ spin-1/2 chain. We prove that these $F$-matrices factorize the tensor…
Applying Baxter's method of the Q-operator to the set of Sekiguchi's commuting partial differential operators we show that Jack polynomials P(x_1,...,x_n) are eigenfunctions of a one-parameter family of integral operators Q_z. The operators…
Using some modification of the standard fermion technique we derive factorized formula for spin operator matrix elements (form-factors) between general eigenstates of the Hamiltonian of quantum Ising chain in a transverse field of finite…
The integrability of the one-dimensional (1D) fermion chain model is investigated in the framework of the Quantum Inverse Scattering Method (QISM). We introduce a new R-operator for the fermion chain model, which is expressed in terms of…
In [1], the spectrum (eigenvalues and eigenstates) of a lattice regularizations of the Sine-Gordon model has been completely characterized in terms of polynomial solutions with certain properties of the Baxter equation. This…
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…