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We study the inner product of Bethe states in the inhomogeneous periodic XXX spin-1/2 chain of length L, which is given by the Slavnov determinant formula. We show that the inner product of an on-shell M-magnon state with a generic M-magnon…

High Energy Physics - Theory · Physics 2015-06-05 Ivan Kostov , Yutaka Matsuo

The problem of separation of variables (SoV) in supersymmetric spin chains is closely related to the calculation of correlation functions in N=4 SYM theory which is integrable in the planar limit. To address this question we find a compact…

High Energy Physics - Theory · Physics 2018-10-02 Nikolay Gromov , Fedor Levkovich-Maslyuk

The algebraic Bethe Ansatz is a prosperous and well-established method for solving one-dimensional quantum models exactly. The solution of the complex eigenvalue problem is thereby reduced to the solution of a set of algebraic equations.…

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

We compute scalar products of off-shell Bethe vectors in models with $o_{2n+1}$ symmetry. The scalar products are expressed as a sum over partitions of the Bethe parameter sets, the building blocks being the so-called highest coefficients.…

Mathematical Physics · Physics 2025-07-23 A. Liashyk , S. Pakuliak , E. Ragoucy

We study integrable models with $\mathfrak{gl}(2|1)$ symmetry and solvable by nested algebraic Bethe ansatz. We obtain a determinant representation for scalar products of Bethe vectors, when the Bethe parameters obey some relations weaker…

Mathematical Physics · Physics 2016-12-21 A. Hutsalyuk , A. Liashyk , S. Z. Pakuliak , E. Ragoucy , N. A. Slavnov

In this note, we study the eigenvectors and the scalar products the integrable long-range deformation of a XXX spin chain which is solved exactly by algebraic Bethe ansatz, and it coincides in the bulk with the Inozemtsev spin chain. At the…

High Energy Physics - Theory · Physics 2015-06-15 D. Serban

The representation of scalar products of Bethe wave functions in terms of the Dual Fields, proven by A.G.Izergin and V.E.Korepin in 1987, plays an important role in the theory of completely integrable models. The proof in \cite{Izergin87}…

High Energy Physics - Theory · Physics 2009-10-22 A. Mikhailov

A probabilistic algorithm for preparing Bethe eigenstates of the spin-1/2 Heisenberg spin chain on a quantum computer has recently been found. We derive an exact formula for the success probability of this algorithm in terms of the Gaudin…

Quantum Physics · Physics 2022-08-24 Wen Li , Mert Okyay , Rafael I. Nepomechie

We consider the problem of computing the overlaps between the Bethe states of the XXZ spin-1/2 chain and generic states. We derive recursive formulas for the overlaps between some simple product states and off-shell Bethe states within the…

Statistical Mechanics · Physics 2016-04-28 Lorenzo Piroli , Pasquale Calabrese

Based on the inhomogeneous T-Q relation constructed via the off-diagonal Bethe Ansatz, the Bethe-type eigenstates of the XXZ spin-1/2 chain with arbitrary boundary fields are constructed. It is found that by employing two sets of gauge…

Mathematical Physics · Physics 2015-05-20 Xin Zhang , Yuan-Yuan Li , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

Spin-flip methods applied to excited-state approaches like the Bethe-Salpeter Equation allow access to the excitation energies of open-shell systems, such as molecules and defects in solids. The eigenstates of these solutions, however, are…

Materials Science · Physics 2024-06-13 Bradford A. Barker , Arabi Seshappan , David A. Strubbe

We consider an $XYZ$ spin chain within the framework of the generalized algebraic Bethe ansatz. We study form factors of local operators corresponding to the singlet states in the limit of free fermions. We obtain explicit representations…

Mathematical Physics · Physics 2023-09-13 G. Kulkarni , N. A. Slavnov

We consider open XXX spins chain with two general boundary matrices submitted to one constraint, which is equivalent to the possibility to put the two matrices in a triangular form. We construct Bethe vectors from a generalized algebraic…

Mathematical Physics · Physics 2015-06-11 S. Belliard , N. Crampe , E. Ragoucy

We study quantum integrable GL(3)-based models with a trigonometric R-matrix solvable by the nested algebraic Bethe ansatz. We derive a determinant representation for a special case of scalar products of Bethe vectors. This representation…

Mathematical Physics · Physics 2015-03-23 N. A. Slavnov

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

We study the scalar product S_{l,m} between an on-shell and an off-shell Bethe state in models with SU(3)-invariance, where l and m denote the cardinalities of the two sets of Bethe roots. We construct recursion relations relating S_{l,m}…

Mathematical Physics · Physics 2015-06-16 M Wheeler

Optical properties of materials related to light absorption and scattering are explained by the excitation of electrons. The Bethe-Salpeter equation is the state-of-the-art approach to describe these processes from first principles (ab…

Numerical Analysis · Mathematics 2020-08-21 Peter Benner , Carolin Penke

We consider the XXZ spin-1/2 Heisenberg chain with antiperiodic boundary conditions. The inhomogeneous version of this model can be solved by Separation of Variables (SoV), and the eigenstates can be constructed in terms of Q-functions,…

Mathematical Physics · Physics 2021-05-07 H. Pei , V. Terras

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

Using considerations based on the thermodynamical Bethe ansatz as well representation theory of twisted Yangians we derive an exact expression for the overlaps between the Bethe eigenstates of the $SO(6)$ spin chain and matrix product…

High Energy Physics - Theory · Physics 2022-07-19 Marius de Leeuw , Tamás Gombor , Charlotte Kristjansen , Georgios Linardopoulos , Balázs Pozsgay