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Related papers: Factorization of R-matrix and Baxter Q-operators f…

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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…

Mathematical Physics · Physics 2009-10-31 A. A. Ovchinnikov

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…

Mathematical Physics · Physics 2015-05-20 Rouven Frassek , Tomasz Lukowski , Carlo Meneghelli , Matthias Staudacher

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…

Mathematical Physics · Physics 2015-06-03 S. G. Mc Ateer , M. Wheeler

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…

High Energy Physics - Theory · Physics 2010-04-05 Wen-Li Yang , Yao-Zhong Zhang

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…

Quantum Algebra · Mathematics 2016-11-23 Atsuo Kuniba

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…

High Energy Physics - Theory · Physics 2014-12-11 Rouven Frassek

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…

Representation Theory · Mathematics 2024-01-23 Muze Ren

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…

Mathematical Physics · Physics 2012-04-18 Vladimir Kazakov , Sebastien Leurent , Zengo Tsuboi

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.…

Mathematical Physics · Physics 2013-07-04 Kohei Motegi

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…

High Energy Physics - Theory · Physics 2008-11-26 S. Derkachov , D. Karakhanyan , R. Kirschner

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…

Quantum Algebra · Mathematics 2007-05-23 S. E. Derkachov

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…

Mathematical Physics · Physics 2013-09-17 Alexander Alexandrov , Vladimir Kazakov , Sebastien Leurent , Zengo Tsuboi , Anton Zabrodin

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…

High Energy Physics - Theory · Physics 2022-11-30 Nikolay Gromov , Nicolo Primi , Paul Ryan

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…

High Energy Physics - Theory · Physics 2026-01-13 P. Antonenko , S. Derkachov , P. Valinevich

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…

Mathematical Physics · Physics 2011-07-13 S. G. Mc Ateer , M. Wheeler

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…

Classical Analysis and ODEs · Mathematics 2015-11-13 Vadim B. Kuznetsov , Vladimir V. Mangazeev , Evgeny K. Sklyanin

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…

Statistical Mechanics · Physics 2011-12-05 N. Iorgov , V. Shadura , Yu. Tykhyy

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…

High Energy Physics - Theory · Physics 2009-10-31 Yukiko Umeno , Masahiro Shiroishi , Miki Wadati

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…

High Energy Physics - Theory · Physics 2010-05-12 G. Niccoli

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…

Statistical Mechanics · Physics 2007-05-23 Shi-shyr Roan