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A second order finite-difference equation has two linearly independent solutions. It is shown here that, like in the continuous case, at most one of the two can be a polynomial solution. The uniqueness in the classical continuous…

Mathematical Physics · Physics 2015-09-18 Alexander Moroz

We investigate the exact overlaps between eigenstates of integrable spin chains and a special class of states called "integrable initial/final states". These states satisfy a special integrability constraint, and they are closely related to…

Statistical Mechanics · Physics 2021-05-05 Tamás Gombor , Balázs Pozsgay

We analyze the ground state of the open spin-1/2 isotropic quantum spin chain with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe…

Mathematical Physics · Physics 2015-06-17 Rafael I. Nepomechie , Chunguang Wang

We study spiky string solutions in AdS3 x S1 that are characterized by two spins S,J as well as winding m in S1 and spike number n. We construct explicitly two-cut solutions by using the SL(2) asymptotic Bethe Ansatz equations at leading…

High Energy Physics - Theory · Physics 2010-05-19 M. Kruczenski , A. Tirziu

At large values of the anisotropy \Delta, the open-boundary Heisenberg spin-1/2 chain has eigenstates displaying localization at the edges. We present a Bethe ansatz description of this `edge-locking' phenomenon in the entire \Delta>1…

Strongly Correlated Electrons · Physics 2013-12-24 Vincenzo Alba , Kush Saha , Masudul Haque

We consider the exact solution of a many-body problem of spin-$s$ particles interacting through an arbitrary U(1) invariant factorizable $S$-matrix. The solution is based on a unified formulation of the quantum inverse scattering method for…

High Energy Physics - Theory · Physics 2008-11-26 C. S. Melo , M. J. Martins

We continue the rigged configurations analysis of the solutions to the Bethe ansatz equations for the spin-1/2 isotropic Heisenberg model. We analyze the non self-conjugate strings of Deguchi-Giri and the counter example for the string…

Mathematical Physics · Physics 2015-04-03 Reiho Sakamoto

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 demonstrate the existence of special phantom excitations for open and periodically closed integrable systems at the example of the $XXZ$ Heisenberg spin chain. The phantom excitations do not contribute to the energy of the Bethe state…

Statistical Mechanics · Physics 2021-10-01 Vladislav Popkov , Xin Zhang , Andreas Klümper

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

Recently, the XXX spin chain with arbitrary boundary fields was successfully solved [1] via the off-diagonal Bethe ansatz method [2]. The correctness and the completeness of this solution were numerically verified by Nepomechie for one…

Statistical Mechanics · Physics 2013-09-26 Yuzhu Jiang , Shuai Cui , Junpeng Cao , Wen-Li Yang , Yupeng Wang

We compute the eigenfunctions and eigenvalues of the periodic integrable spin s XXX model using the coordinate Bethe ansatz. To do so, we compute explicitly the Hamiltonian of the model. These results generalize what has been obtained for…

Mathematical Physics · Physics 2011-01-13 Nicolas Crampé , Eric Ragoucy , Ludovic Alonzi

Establishing the completeness of a Bethe Ansatz solution for an exactly solved model is a perennial challenge, which is typically approached on a case by case basis. For the rational, spin-1/2 Richardson--Gaudin system it will be argued…

Exactly Solvable and Integrable Systems · Physics 2017-10-19 Jon Links

A non homogeneous spin chain in the representations $ \{3 \}$ and $ \{3^*\}$ of $A_2$ is analyzed. We find that the naive nested Bethe ansatz is not applicable to this case. A method inspired in the nested Bethe ansatz, that can be applied…

High Energy Physics - Theory · Physics 2009-10-30 Julio Abad , Miguel Rios

We find an analytic solution of the Bethe Ansatz equations (BAE) for the special case of a finite XXZ spin chain with free boundary conditions and with a complex surface field which provides for $U_q(sl(2))$ symmetry of the Hamiltonian.…

Exactly Solvable and Integrable Systems · Physics 2015-06-26 V. Fridkin , Yu. Stroganov , D. Zagier

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 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 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

We study spiky strings in the context of the SL(2) Bethe ansatz equations. We find an asymmetric distribution of Bethe roots along one cut that determines the all loop anomalous dimension at leading and subleading orders in a large S…

High Energy Physics - Theory · Physics 2015-05-13 L. Freyhult , M. Kruczenski , A. Tirziu

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