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Related papers: Bethe's Quantum Numbers And Rigged Configurations

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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 examine the question of whether Bethe's ansatz reproduces all states in the periodic Heisenberg XXZ and XXX spin chains. As was known to Bethe himself, there are states for which the Bethe momenta $k_n$ diverge: these are in fact the…

Strongly Correlated Electrons · Physics 2007-05-23 Rahul Siddharthan

Bethe equations, whose solutions determine exact eigenvalues and eigenstates of corresponding integrable Hamiltonians, are generally hard to solve. We implement a Variational Quantum Eigensolver (VQE) approach to estimating Bethe roots of…

Quantum Physics · Physics 2025-01-28 David Raveh , Rafael I. Nepomechie

We present a counting formula that relates the number of physical Bethe states of integrable models with a twisted boundary condition to the number of states in the untwisted or partially twisted limit.

Mathematical Physics · Physics 2025-04-30 Hongfei Shu , Peng Zhao , Rui-Dong Zhu , Hao Zou

We count the Bethe states of quantum integrable models with twisted boundary conditions using the Witten index of 2d supersymmetric gauge theories. For multi-component models solvable by the nested Bethe ansatz, the result is a novel…

High Energy Physics - Theory · Physics 2023-10-12 Hongfei Shu , Peng Zhao , Rui-Dong Zhu , Hao Zou

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

The string hypothesis of Bethe roots is a cornerstone in the thermodynamic analysis of quantum integrable systems, since it connects root configurations with physical quantities such as the ground-state energy, surface energy and excitation…

Mathematical Physics · Physics 2026-05-29 Zhouzheng Ji , Pei Sun , Xiaotian Xu , Yi Qiao , Junpeng Cao , Wen-Li Yang

We develop a new method to compute the exact overlaps between integrable boundary states and on-shell Bethe states for integrable spin chains. Our method is based on the coordinate Bethe Ansatz and does not rely on the "rotation trick" of…

Statistical Mechanics · Physics 2020-06-24 Yunfeng Jiang , Balázs Pozsgay

The one-dimensional Hubbard model with arbitrary boundary magnetic fields is solved exactly via the Bethe ansatz methods. With the coordinate Bethe ansatz in the charge sector, the second eigenvalue problem associated with the spin sector…

Strongly Correlated Electrons · Physics 2015-06-17 Yuan-Yuan Li , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

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 construction of analytic solutions for quasi-exactly solvable systems is an interesting problem. We revisit a class of models for which the odd solutions were largely missed previously in the literature: the anharmonic oscillator, the…

Mathematical Physics · Physics 2024-09-17 Siyu Li , Ian Marquette , Yao-Zhong Zhang

The procedure for obtaining integrable open spin chain Hamiltonians via reflection matrices is explicitly carried out for some three-state vertex models. We have considered the 19-vertex models of Zamolodchikov-Fateev and Izergin-Korepin,…

Exactly Solvable and Integrable Systems · Physics 2014-11-18 E. C. Fireman , A. Lima-Santos , W. Utiel

We give a brief review on the use of Bethe ansatz techniques to construct solutions of recursive functional equations which emerged in a bootstrap approach to the quantum Ernst system. The construction involves two particular limits of a…

Mathematical Physics · Physics 2009-10-31 M. Niedermaier , H. Samtleben

We study the spectrum of the integrable open XXX Heisenberg spin chain subject to non-diagonal boundary magnetic fields. The spectral problem for this model can be formulated in terms of functional equations obtained by separation of…

Statistical Mechanics · Physics 2011-03-07 Holger Frahm , Jan H. Grelik , Alexander Seel , Tobias Wirth

It is known that for the Heisenberg XXZ spin-$\frac{1}{2}$ chain in the critical regime, the scaling limit of the vacuum Bethe roots yields an infinite set of numbers that coincide with the energy spectrum of the quantum mechanical 3D…

Mathematical Physics · Physics 2024-07-23 Sascha Gehrmann , Gleb A. Kotousov , Sergei L. Lukyanov

The distribution of Bethe roots, solution of the inhomogeneous Bethe equations, which characterize the ground state of the periodic XXX Heisenberg spin-$\frac{1}{2}$ chain is investigated. Numerical calculations shows that, for this state,…

Mathematical Physics · Physics 2018-06-20 S. Belliard , A. Faribault

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

The rational $Q$-system is an efficient method to solve Bethe ansatz equations for quantum integrable spin chains. We construct the rational $Q$-systems for generic Bethe ansatz equations described by an $A_{\ell-1}$ quiver, which include…

High Energy Physics - Theory · Physics 2023-03-15 Jie Gu , Yunfeng Jiang , Marcus Sperling

We reexamine Bethe ansatz solutions of the massive Thirring model. We solve equations of periodic boundary conditions numerically without referring to the density of states. It is found that there is only one bound state in the massive…

High Energy Physics - Theory · Physics 2014-11-18 Takehisa Fujita , Kenji Yamamoto , Yasuyuki Sekiguchi

The Bethe ansatz solutions for an open XXZ spin chain with arbitrary spin with N sites and nondiagonal boundary terms are revisited. The anisotropy parameter, for cases considered here, has values \eta = i \pi r/q, where r and q are…

Mathematical Physics · Physics 2015-06-19 Rajan Murgan , Christopher Silverthorn