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Related papers: An exact solution to asymptotic Bethe equation

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We investigate the pseudospin symmetry case of a spin-1/2 particle governed by the generalized isotonic oscillator, by presenting quasi exact polynomial solutions to Dirac equation with pseudospin symmetry vector and scalar potentials. The…

Mathematical Physics · Physics 2015-06-05 D. Agboola

We investigate Bethe Ansatz equations for the one-dimensional spin-$\frac{1}{2}$ Heisenberg XXX chain with a special interest in a finite system. Solutions for the two-particle sector are obtained. The ground state in antiferromagnetic case…

Condensed Matter · Physics 2007-05-23 Shao-shiung Lin , Shi-shyr Roan

We present asymptotically exact solutions of an incommensurate Harper equation---one-dimensional Schroedinger equation of one particle on a lattice in a cosine potential. The wave functions can be written as an infinite product of string…

Condensed Matter · Physics 2009-10-31 A. G. Abanov , J. C. Talstra , P. B. Wiegmann

We investigate special solutions to the Bethe Ansatz equations (BAE) for open integrable $XXZ$ Heisenberg spin chains containing phantom (infinite) Bethe roots. The phantom Bethe roots do not contribute to the energy of the Bethe state, so…

Statistical Mechanics · Physics 2021-03-24 Xin Zhang , Andreas Klümper , Vladislav Popkov

Using Jacobi elliptic function addition formulas and summation identities we obtain several static and moving periodic soliton solutions of a classical anisotropic, discrete Heisenberg spin chain with and without an external magnetic field.…

Exactly Solvable and Integrable Systems · Physics 2009-11-13 M. Lakshmanan , Avadh Saxena

We consider the open spin-s XXZ quantum spin chain with N sites and general integrable boundary terms for generic values of the bulk anisotropy parameter, and for values of the boundary parameters which satisfy a certain constraint. We…

Mathematical Physics · Physics 2010-04-08 Luc Frappat , Rafael Nepomechie , Eric Ragoucy

We investigate spin-1/2 electrons with local Hubbard interaction and variable range hopping amplitudes which decay like~$\sinh(\kappa)/\sinh(\kappa r)$. Assuming integrability the Asymptotic Bethe Ansatz approach allows us to derive the…

Condensed Matter · Physics 2012-07-07 F. Gebhard , P. -A. Bares

Boundary driven quantum master equation for a general inhomogeneous (non-integrable) anisotropic Heisenberg spin $1/2$ chain, or an equivalent nearest neighbor interacting spinless fermion chain, is considered in the presence of a strong…

Strongly Correlated Electrons · Physics 2015-05-04 Zala Lenarčič , Tomaž Prosen

The quasiclassical asymptotics of the Knizhnik-Zamolodchikov system is studied. Solutions to this system in this limit are related naturally to Bethe vectors in the Gaudin model of spin chains.

High Energy Physics - Theory · Physics 2008-02-03 Nicolai Reshetikhin , Alexander Varchenko

A generalized inhomogeneous higher-order nonlinear Schrodinger (GIHNLS) equation for the Heisenberg ferromagnetic spin chain system in (1+1)-dimensions under zero boundary condition at infinity is taken into account. The spectral analysis…

Exactly Solvable and Integrable Systems · Physics 2022-08-26 Zhou-Zheng Kang , Rong-Cao Yang

We derive a non-linear integral equation for the Bethe-ansatz solvable open XXZ spin chain of arbitrary length describing the lowest lying state with zero magnetization. For this case we show how to combine the integral representation with…

Mathematical Physics · Physics 2009-02-19 A. Seel , T. Wirth

The off-diagonal Bethe ansatz method is generalized to the high spin integrable systems associated with the su(2) algebra by employing the spin-s isotropic Heisenberg chain model with generic integrable boundaries as an example. With the…

Statistical Mechanics · Physics 2015-06-19 Junpeng Cao , Shuai Cui , Wen-Li Yang , Kangjie Shi , Yupeng Wang

Spin models like the Heisenberg Hamiltonian effectively describe the interactions of open-shell transition-metal ions on a lattice and can account for various properties of magnetic solids and molecules. Numerical methods are usually…

Strongly Correlated Electrons · Physics 2025-06-24 Shadan Ghassemi Tabrizi , Thomas D. Kühne

An integrable anisotropic Heisenberg spin chain with nearest-neighbour couplings, next-nearest-neighbour couplings and scalar chirality terms is constructed. After proving the integrability, we obtain the exact solution of the system. The…

Mathematical Physics · Physics 2020-06-03 Yi Qiao , Pei Sun , Zhirong Xin , Junpeng Cao , Wen-Li Yang

The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex model with fixed open boundary conditions and the corresponding $SU_{q}(n)$ invariant…

High Energy Physics - Theory · Physics 2009-10-22 H. J. de Vega , A. González--Ruiz

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 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

In this paper, nonlinear equations describing one-dimensional non-Heisenberg ferromagnetic model are studied by use of generalized coherent states in a real parameterization. Also dissipative spin wave equation for dipole and quadruple…

Strongly Correlated Electrons · Physics 2012-01-17 Khikmat Kh. Muminov , Yousef Yousefi

We investigate the strong asymptotics of Heine-Stieltjes polynomials - polynomial solutions of a second order differential equations with complex polynomial coefficients. The solution is given in terms of critical measures (saddle points of…

Classical Analysis and ODEs · Mathematics 2009-03-17 A. Martinez-Finkelshtein , E. A. Rakhmanov

Asymptotic solutions to the quantized Knizhnik-Zamolodchikov equation associated with $\frak{gl}_{N+1}$ are constructed. The leading term of an asymptotic solution is the Bethe vector -- an eigenvector of the transfer-matrix of a quantum…

High Energy Physics - Theory · Physics 2008-02-03 Vitaly Tarasov , Alexander Varchenko