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Related papers: On Generalized $Q$-systems

200 papers

The $Q$-system is an efficient method for finding complete physical solutions of Bethe ansatz equations, but so far its application has been confined to systems possessing $U(1)$ symmetry. We extend the rational $Q$-system framework to…

High Energy Physics - Theory · Physics 2025-12-02 Yunfeng Jiang , Yi-Chao Liu , Yuan Miao , Zi-Xi Tan

We have recently constructed a large class of open quantum spin chains which have quantum-algebra symmetry and which are integrable. We show here that these models can be exactly solved using a generalization of the analytical Bethe Ansatz…

High Energy Physics - Theory · Physics 2014-11-18 Luca Mezincescu , Rafael I. Nepomechie

We propose a Bethe-Ansatz-type solution of the open spin-1/2 integrable XXZ quantum spin chain with general integrable boundary terms and bulk anisotropy values i \pi/(p+1), where p is a positive integer. All six boundary parameters are…

High Energy Physics - Theory · Physics 2011-02-16 Rajan Murgan , Rafael I. Nepomechie , Chi Shi

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

Bethe ansatz equations for spin-$s$ Heisenberg spin chain with $s\ge1$ are significantly more difficult to analyze than the spin-$\tfrac{1}{2}$ case, due to the presence of repeated roots. As a result, it is challenging to derive extra…

High Energy Physics - Theory · Physics 2024-05-01 Jue Hou , Yunfeng Jiang , Rui-Dong Zhu

Q-systems provide an efficient way of solving Bethe equations. We formulate here Q-systems for both the isotropic and anisotropic open Heisenberg quantum spin-1/2 chains with diagonal boundary magnetic fields. We check these Q-systems using…

High Energy Physics - Theory · Physics 2020-08-26 Rafael I. Nepomechie

We consider the sl(2)_q-invariant open spin-1/2 XXZ quantum spin chain of finite length N. For the case that q is a root of unity, we propose a formula for the number of admissible solutions of the Bethe ansatz equations in terms of…

Mathematical Physics · Physics 2017-05-24 Azat M. Gainutdinov , Wenrui Hao , Rafael I. Nepomechie , Andrew J. Sommese

We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary terms. By exploiting certain functional relations at roots of unity, we derive a generalized form of T-Q relation involving more than one independent Q(u), which…

Mathematical Physics · Physics 2015-06-05 Rashad Baiyasi , Rajan Murgan

We briefly review Bethe Ansatz solutions of the integrable open spin-1/2 XXZ quantum spin chain derived from functional relations obeyed by the transfer matrix at roots of unity.

High Energy Physics - Theory · Physics 2007-05-23 Rafael I. Nepomechie

The open spin-1/2 XXZ spin chain with diagonal boundary magnetic fields is the paradigmatic example of a quantum integrable model with open boundary conditions. We formulate a quantum algorithm for preparing Bethe states of this model,…

Quantum Physics · Physics 2022-01-26 John S. Van Dyke , Edwin Barnes , Sophia E. Economou , Rafael I. Nepomechie

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

With the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the $XXX$ spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer…

Mathematical Physics · Physics 2015-06-16 Junpeng Cao , Wenli Yang , Kangjie Shi , Yupeng Wang

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

Q-systems first appeared in the analysis of the Bethe equations for the XXX-model and generalized Heisenberg spin chains. Such systems are known to exist for any simple Lie algebra and many other Kac-Moody algebras. We formulate the…

Representation Theory · Mathematics 2008-11-26 Rinat Kedem

The full set of polynomial solutions of the nested Bethe Ansatz is constructed for the case of A_2 rational spin chain. The structure and properties of these associated solutions are more various then in the case of usual XXX (A_1) spin…

High Energy Physics - Theory · Physics 2009-10-31 G. P. Pronko , Yu. G. Stroganov

We analyse the famous Baxter's $T-Q$ equations for $XXX$ ($XXZ$) spin chain and show that apart from its usual polynomial (trigonometric) solution, which provides the solution of Bethe-Ansatz equations, there exists also the second solution…

High Energy Physics - Theory · Physics 2008-11-26 G. P. Pronko , Yu. G. Stroganov

We introduce a generalization of the original Coordinate Bethe Ansatz that allows to treat the case of open spin chains with non-diagonal boundary matrices. We illustrate it on two cases: the XXX and XXZ chains. Short review on a joint work…

High Energy Physics - Theory · Physics 2015-05-30 E. Ragoucy

We construct a Q-operator for the open XXZ Heisenberg quantum spin chain with diagonal boundary conditions and give a rigorous derivation of Baxter's TQ relation. Key roles in the theory are played by a particular infinite-dimensional…

Mathematical Physics · Physics 2020-10-13 Bart Vlaar , Robert Weston

A quantum algebra invariant integrable closed spin 1 chain is introduced and analysed in detail. The Bethe ansatz equations as well as the energy eigenvalues of the model are obtained. The highest weight property of the Bethe vectors with…

solv-int · Physics 2015-06-26 Jon Links , Angela Foerster , Michael Karowski

In this note we construct Q-operators for the spin s open Heisenberg XXX chain with diagonal boundaries in the framework of the quantum inverse scattering method. Following the algebraic Bethe ansatz we diagonalise the introduced…

Mathematical Physics · Physics 2023-01-04 Rouven Frassek , István M. Szécsényi
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