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We study the largest particle-number-preserving sector of the dilatation operator in maximally supersymmetric gauge theory. After exploring one-loop Bethe Ansatze for the underlying spin chain with psl(2|2) symmetry for simple root systems…

High Energy Physics - Theory · Physics 2008-11-26 A. V. Belitsky

We conjecture a new way to construct eigenstates of integrable XXX quantum spin chains with SU(N) symmetry. The states are built by repeatedly acting on the vacuum with a single operator Bgood(u) evaluated at the Bethe roots. Our proposal…

High Energy Physics - Theory · Physics 2019-08-13 Nikolay Gromov , Fedor Levkovich-Maslyuk , Grigory Sizov

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

The general expression for the local matrix $L(\theta)$ of a quantum chain with the site space in any representation of $su(3)$ is obtained. This is made by generalizing $L(\theta)$ from the fundamental representation and imposing the…

Condensed Matter · Physics 2016-08-31 J. Abad , M. Rios

We describe a simple quantum mechanical method that can be used to obtain accurate numerical results over long time scales for the spin correlation tensor of an electron spin that is hyperfine coupled to a large number of nuclear spins.…

Quantum Physics · Physics 2018-08-13 Lachlan P. Lindoy , David E. Manolopoulos

In integrable spin chains, the spectral problem can be solved by the method of Bethe ansatz, which transforms the problem of diagonalization of the Hamiltonian into the problem of solving a set of algebraic equations named Bethe equations.…

High Energy Physics - Theory · Physics 2025-08-27 Yi-Jun He , Jue Hou , Yi-Chao Liu , Zi-Xi Tan

A quantum integrable spin chain model associated with the $G_2$ exceptional Lie algebra is studied. By using the fusion technique, the closed recursive relations among the fused transfer matrices are obtained. These identities allow us to…

Mathematical Physics · Physics 2024-12-18 Guang-Liang Li , Junpeng Cao , Pei Sun , Wen-Li Yang , Kangjie Shi , Yupeng Wang

Extending the method proposed in [arXiv:1109.5524], we derive QQ-relations (functional relations among Baxter Q-functions) and T-functions (eigenvalues of transfer matrices) for fusion vertex models associated with the twisted quantum…

Mathematical Physics · Physics 2024-07-15 Zengo Tsuboi

We propose that Baxter's Z-invariant six-vertex model at the rational gl(2) point on a planar but in general not rectangular lattice provides a way to study Yangian invariants. These are identified with eigenfunctions of certain monodromies…

Mathematical Physics · Physics 2014-04-15 Rouven Frassek , Nils Kanning , Yumi Ko , Matthias Staudacher

We propose a new framework for the nested algebraic Bethe ansatz for a closed, rational spin chain with $\mathfrak{g}$-symmetry for any simple Lie algebra $\mathfrak{g}$. Starting the nesting process by removing a single simple root from…

Mathematical Physics · Physics 2024-06-12 Allan John Gerrard

The integrable XXZ alternating spin chain with generic non-diagonal boundary terms specified by the most general non-diagonal K-matrices is studied via the off-diagonal Bethe Ansatz method. Based on the intrinsic properties of the fused…

Statistical Mechanics · Physics 2015-07-16 Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We formulate $Q$-systems for the closed XXZ, open XXX and open quantum-group-invariant XXZ quantum spin chains. Polynomial solutions of these $Q$-systems can be found efficiently, which in turn lead directly to the admissible solutions of…

High Energy Physics - Theory · Physics 2021-05-19 Zoltán Bajnok , Etienne Granet , Jesper Lykke Jacobsen , Rafael I. Nepomechie

This PhD thesis explores the similarities between integrable spin chains and quantum field theories, such as Super Yang Mills. We first study integrable spin chains and build explicitly a polynomial "Backlund flow" and polynomial…

High Energy Physics - Theory · Physics 2015-03-20 Sebastien Leurent

The general rational solution of the Yang-Baxter equation with the symmetry algebra sl(2) can be represented as the product of the simpler building blocks denoted as R-operators. The R-operators are constructed explicitly and have simple…

Quantum Algebra · Mathematics 2009-01-08 S. E. Derkachov

We derive exactly scalar products and form factors for integrable higher-spin XXZ chains through the algebraic Bethe-ansatz method. Here spin values are arbitrary and different spins can be mixed. We show the affine quantum-group symmetry,…

Statistical Mechanics · Physics 2011-07-06 Tetsuo Deguchi , Chihiro Matsui

We propose commuting sets of matrix-valued difference operators in terms of trigonometric ${\rm GL}(N|M)$-valued $R$-matrices thus providing quantum supersymmetric (and possibly anisotropic) spin Ruijsenaars-Macdonald operators. Two types…

Mathematical Physics · Physics 2024-03-05 M. Matushko , A. Zotov

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 consider an open spin chain model with GL(N) bulk symmetry that is broken to GL(M) x GL(N-M) by the boundary, which is a generalization of a model arising in string/gauge theory. We prove the integrability of this model by constructing…

High Energy Physics - Theory · Physics 2015-05-14 Rafael I. Nepomechie

We study integrable lattice regularizations of the sine-Gordon model with the help of the separation of variables method of Sklyanin and the Baxter Q-operators. This leads us to the complete characterization of the spectrum (eigenvalues and…

High Energy Physics - Theory · Physics 2011-02-16 G. Niccoli , J. Teschner

We develop a systematic approach to compute physical observables of integrable spin chains with finite length. Our method is based on Bethe ansatz solution of the integrable spin chain and computational algebraic geometry. The final results…

High Energy Physics - Theory · Physics 2021-09-23 Yunfeng Jiang , Rui Wen , Yang Zhang