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Related papers: Universal Baxter TQ-relations for open boundary qu…

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Let $A_q$ be the alternating central extension of the q-Onsager algebra, a comodule algebra over the quantum loop algebra of $sl_2$. We classify one-dimensional representations of $A_q$, and show that spin-j K-operators constructed in…

Quantum Algebra · Mathematics 2026-04-17 Pascal Baseilhac , Azat M. Gainutdinov , Guillaume Lemarthe

Corresponding to the Izergin-Korepin (A_2^(2)) R matrix, there are three diagonal solutions (``K matrices'') of the boundary Yang-Baxter equation. Using these R and K matrices, one can construct transfer matrices for open integrable quantum…

High Energy Physics - Theory · Physics 2009-10-31 Rafael I. Nepomechie

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

Integrable open-boundary condition for the q-deformed Essler-Korepin-Schoutens extended Hubbard model of strongly correlated electrons, are studied in the framework of the boundary quantum inverse scattering method. Diagonal boundary…

Strongly Correlated Electrons · Physics 2009-10-31 Xiang-Yu Ge

Baxter's Q-operator for the quantum transfer matrix of the XXZ spin-chain is constructed employing the representation theory of quantum groups. The spectrum of this Q-operator is discussed and novel functional relations which describe the…

Mathematical Physics · Physics 2007-05-23 Christian Korff

We construct Baxter operators for the homogeneous closed $\mathrm{XXX}$ spin chain with the quantum space carrying infinite or finite dimensional $s\ell_2$ representations. All algebraic relations of Baxter operators and transfer matrices…

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

Baxter's TQ-equation is solved for the six-vertex model using the representation theory of quantum groups at roots of unity. A novel simplified construction of the Q-operator is given depending on a new free parameter. Specializing this…

Mathematical Physics · Physics 2007-05-23 Christian Korff

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…

High Energy Physics - Theory · Physics 2011-03-03 Vladimir V. Bazhanov , Tomasz Lukowski , Carlo Meneghelli , Matthias Staudacher

Baxter's $T-Q$ relation for the periodic spin-$\frac12$ XYZ chain is studied. We extensively perform numerical calculations for the $T-Q$ relation and the Bethe ansatz equations. Numerical based hypotheses are then proposed to answer some…

Mathematical Physics · Physics 2024-04-22 Xin Zhang

In this paper we propose algebraic universal procedure for deriving "fusion rules" and Baxter equation for any integrable model with $U_q(\widehat{sl}_2)$ symmetry of Quantum Inverse Scattering Method. Universal Baxter Q- operator is got…

High Energy Physics - Theory · Physics 2009-10-30 Alexander Antonov , Boris Feigin

In this paper we discuss some properties of Baxter's TQ equation for the eight-vertex elliptic Sklyanin algebra it its compact representation based on the elliptic Gamma-functions. As the main result, we establish the structure of the…

Mathematical Physics · Physics 2023-04-03 Sergey Sergeev

The Yang-Baxter equation and it's various forms have applications in many fields, including statistical mechanics, knot theory, and quantum information. Unitary solutions of the braided Yang-Baxter equation are of particular interest as…

Quantum Physics · Physics 2023-04-04 David Lovitz

In this paper, we address the problem of Yang-Baxter integrability of doubled quantum circuit of qubits (spins 1/2) with open boundary conditions where the two circuit replicas are only coupled at the left or right boundary. We investigate…

Quantum Physics · Physics 2025-01-22 Chiara Paletta , Tomaž Prosen

Generalized Baxter's relations on the transfer-matrices (also known as Baxter's TQ relations) are constructed and proved for an arbitrary untwisted quantum affine algebra. Moreover, we interpret them as relations in the Grothendieck ring of…

Quantum Algebra · Mathematics 2015-11-04 Edward Frenkel , David Hernandez

In this article we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are essentially described by the Yang-Baxter and boundary…

Mathematical Physics · Physics 2010-09-29 Anastasia Doikou , Stefano Evangelisti , Giovanni Feverati , Nikos Karaiskos

We study the diagonalization problem of certain discrete quantum integrable models by the method of Baxter's T-Q relation from the algebraic geometry aspect. Among those the Hofstadter type model (with the rational magnetic flux), discrete…

High Energy Physics - Theory · Physics 2009-11-07 Shao-shiung Lin , Shi-shyr Roan

We study an integrable noncompact superspin chain model that emerged in recent studies of the dilatation operator in the N=1 super-Yang-Mills theory. It was found that the latter can be mapped into a homogeneous Heisenberg magnet with the…

High Energy Physics - Theory · Physics 2011-02-16 A. V. Belitsky , S. E. Derkachov , G. P. Korchemsky , A. N. Manashov

We review recent results on the Bethe Ansatz solutions for the eigenvalues of the transfer matrix of an integrable open XXZ quantum spin chain using functional relations which the transfer matrix obeys at roots of unity. First, we consider…

High Energy Physics - Theory · Physics 2008-11-26 Rajan Murgan

Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to 3/2 are given. Relations between Hamiltonians for some U_q(sl_2)-symmetric and U(1)-symmetric…

High Energy Physics - Theory · Physics 2009-11-07 Andrei G. Bytsko

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