English
Related papers

Related papers: A Q-operator for open spin chains I: Baxter's TQ r…

200 papers

We describe the Algebraic Bethe Ansatz for the spin-1/2 XXX and XXZ Heisenberg chains with open and periodic boundary conditions in terms of tensor networks. These Bethe eigenstates have the structure of Matrix Product States with a…

Strongly Correlated Electrons · Physics 2012-07-23 Valentin Murg , Vladimir E. Korepin , Frank Verstraete

An explicit construction for Q-operators of the finite XXZ spin-chain with twisted boundary conditions is presented. The massless and the massive regime is considered as well as the root of unity case. It is explained how these results…

High Energy Physics - Theory · Physics 2014-11-18 Christian Korff

We use the algebraic Bethe ansatz to obtain the eigenvalues and eigenvectors of the spin-1 Temperley-Lieb open quantum chain with "free" boundary conditions. We exploit the associated reflection algebra in order to prove the off-shell…

Mathematical Physics · Physics 2016-10-04 Rafael I. Nepomechie , Rodrigo A. Pimenta

We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains.…

Mathematical Physics · Physics 2017-03-17 N. Kitanine , J. -M. Maillet , G. Niccoli

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 solve the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups ${\cal U}% _{q}(X_{n})$ for $X_{n}=A_{1},$ $B_{n},$ $C_{n}$ and $D_{n}$. The tool is a modified version…

Exactly Solvable and Integrable Systems · Physics 2016-12-28 R. C. T. Ghiotto , A. L. Malvezzi

The scalar products, form factors and correlation functions of the XXZ spin chain with twisted (or antiperiodic) boundary condition are obtained based on the inhomogeneous $T-Q$ relation and the Bethe states constructed via the off-diagonal…

Mathematical Physics · Physics 2020-03-10 Yi Qiao , Zhirong Xin , Xiaotian Xu , Kun Hao , Tao Yang , Junpeng Cao , Wen-Li Yang

We prove the modified algebraic Bethe Ansatz characterization of the spectral problem for the closed XXX Heisenberg spin chain with an arbitrary twist and arbitrary positive (half)-integer spin at each site of the chain. We provide two…

Mathematical Physics · Physics 2019-09-09 Samuel Belliard , Nikita A. Slavnov , Benoit Vallet

We consider the integrable open XX quantum spin chain with nondiagonal boundary terms. We derive an exact inversion identity, using which we obtain the eigenvalues of the transfer matrix and the Bethe Ansatz equations. For generic values of…

High Energy Physics - Theory · Physics 2008-11-26 Rafael I. Nepomechie

We propose a set of conventional Bethe Ansatz equations and a corresponding expression for the eigenvalues of the transfer matrix for the open spin-1/2 XXZ quantum spin chain with nondiagonal boundary terms, provided that the boundary…

High Energy Physics - Theory · Physics 2008-11-26 Rafael I. Nepomechie

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 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 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

We consider irreducible cyclic representations of the algebra of monodromy matrices corresponding to the R-matrix of the six-vertex model. In roots of unity the Baxter Q-operator can be represented as a trace of a tensor product of…

High Energy Physics - Theory · Physics 2007-05-23 A. A. Belavin , A. V. Odesskii , R. A. Usmanov

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

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

We use the structural similarity of certain Coxeter Artin Systems to the Yang--Baxter and Reflection Equations to convert representations of these systems into new solutions of the Reflection Equation. We construct certain Bethe ansatz…

High Energy Physics - Theory · Physics 2008-11-26 A Doikou , P P Martin

We prove that physical solutions to the Heisenberg spin chain Bethe ansatz equations are exactly obtained by imposing two zero-remainder conditions. This bridges the gap between different criteria, yielding an alternative proof of a…

High Energy Physics - Theory · Physics 2021-05-19 Etienne Granet , Jesper Lykke Jacobsen

We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes…

Mathematical Physics · Physics 2013-11-25 Samuel Belliard , Nicolas Crampé

The spectral properties of operators formed from generators of the q-Onsager non-Abelian infinite dimensional algebra are investigated. Using a suitable functional representation, all eigenfunctions are shown to obey a second-order…

Mathematical Physics · Physics 2009-11-11 Pascal Baseilhac