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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 propose the full system of Baxter Q-functions (QQ-system) for the integrable spin chains with the symmetry of the $D_r$ Lie algebra. We use this QQ-system to derive new Weyl-type formulas expressing transfer matrices in all symmetric and…

High Energy Physics - Theory · Physics 2021-03-17 Gwenaël Ferrando , Rouven Frassek , Vladimir Kazakov

The off-diagonal Bethe Ansatz method [1] is used to revisit the periodic XXX Heisenberg spin-1/2 chain. It is found that the spectrum of the transfer matrix can be characterized by an inhomogeneous T-Q relation, a natural but nontrivial…

Mathematical Physics · Physics 2015-06-09 Yupeng Wang , Wen-Li Yang , Junpeng Cao , Kangjie Shi

We construct Baxter operators as generalized transfer matrices being traces of products of generic $R$ matrices. The latter are shown to factorize into simpler operators allowing for explicit expressions in terms of functions of a Weyl pair…

High Energy Physics - Theory · Physics 2009-11-11 S. Derkachov , D. Karakhanyan , R. Kirschner

We connect two alternative concepts of solving integrable models, Baxter's method of auxiliary matrices (or Q-operators) and the algebraic Bethe ansatz. The main steps of the calculation are performed in a general setting and a formula for…

Mathematical Physics · Physics 2009-11-10 Christian Korff

We develop an approach for constructing the Baxter Q-operators for generic sl(N) spin chains. The key element of our approach is the possibility to represent a solution of the the Yang Baxter equation in the factorized form. We prove that…

Exactly Solvable and Integrable Systems · Physics 2009-02-12 S. E. Derkachov , A. N. Manashov

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

The one-dimensional Heisenberg XXX spin chain appears in a special limit of the AdS/CFT integrable system. We review various ways of proving its integrability, and discuss the associated methods of solution. In particular, we outline the…

High Energy Physics - Theory · Physics 2015-05-20 Matthias Staudacher

For quantum integrable models with elliptic R-matrix, we construct the Baxter Q-operator in infinite-dimensional representations of the algebra of observables.

Quantum Algebra · Mathematics 2008-11-26 A. Zabrodin

We suggest the procedure of the construction of Baxter Q-operators for Toda chain . Apart from the one-paramitric family of Q-operators, considered in our recent paper (hep-th/9908179) we also give the construction of two basic Q-operators…

Exactly Solvable and Integrable Systems · Physics 2009-10-31 G. P. Pronko

We continue our systematic construction of Baxter Q-operators for spin chains, which is based on certain degenerate solutions of the Yang-Baxter equation. Here we generalize our approach from the fundamental representation of gl(n) to…

Mathematical Physics · Physics 2011-12-16 Rouven Frassek , Tomasz Lukowski , Carlo Meneghelli , Matthias Staudacher

The off-diagonal Bethe ansatz method is generalized to the high spin integrable systems associated with the su(2) algebra by employing the spin-s isotropic Heisenberg chain model with generic integrable boundaries as an example. With the…

Statistical Mechanics · Physics 2015-06-19 Junpeng Cao , Shuai Cui , Wen-Li Yang , Kangjie Shi , Yupeng Wang

Baxter operators are constructed for quantum spin chains with deformed $s\ell_2$ symmetry. The parallel treatment of Yang-Baxter operators for the cases of undeformed, trigonometrically and elliptically deformed symmetries presented earlier…

Mathematical Physics · Physics 2015-06-12 D. Chicherin , S. Derkachov , D. Karakhanyan , R. Kirschner

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

In this paper we continue the study of $Q$-operators in the six-vertex model and its higher spin generalizations. In [1] we derived a new expression for the higher spin $R$-matrix associated with the affine quantum algebra…

Mathematical Physics · Physics 2014-07-16 Vladimir V. Mangazeev

We present an approach to evaluate the full operatorial Q-system of all $\mathfrak{u}(p,q|r+s)$-invariant spin chains with representations of Jordan-Schwinger type. In particular, this includes the super spin chain of planar $\mathcal{N}=4$…

High Energy Physics - Theory · Physics 2017-10-31 Rouven Frassek , Christian Marboe , David Meidinger

In this paper, we look at the asymmetric simple exclusion process with open boundaries with a current-counting deformation. We construct a two-parameter family of transfer matrices which commute with the deformed Markov matrix of the…

Mathematical Physics · Physics 2014-07-11 Alexandre Lazarescu , Vincent Pasquier

We discuss how the shift operator and the Hamiltonian enter the hierarchy of Baxter Q-operators in the example of gl(n) homogeneous spin-chains. Building on the construction that was recently carried out by the authors and their…

High Energy Physics - Theory · Physics 2013-02-25 Rouven Frassek , Carlo Meneghelli

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…

Mathematical Physics · Physics 2008-11-26 Marco Rossi , Robert Weston

This paper presents the second part of our study devoted to the construction of Baxter operators for the homogeneous closed XXX spin chain with the quantum space carrying infinite or finite-dimensional $s\ell_2$ representations. We consider…

High Energy Physics - Theory · Physics 2015-05-28 D. Chicherin , S. Derkachov , D. Karakhanyan , R. Kirschner