Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1609.07941

Bethe Ansatz approach to the three-magnon problem in an infinite $XX$ spin chain with Izing next neighboring ferromagnetic interaction

P. N. Bibikov

Published Sep 26, 2016• 0 citations
arXivHTMLPDF

Abstract

Using the traditional and degenerative discrete-diffractive versions of Bethe Ansatz we construct a rude set of three-magnon states in the infinite $XX$ spin chain with Izing next neighboring ferromagnetic term.

DOI
10.48550/arxiv.1609.07941

Related papers

Three magnons in an isotropic S = 1 ferromagnetic chain as an exactly solvable non-integrable system

P N Bibikov

Abstract It is shown that a generalization of the Bethe ansatz based on a utilization of degenerative discrete-diffractive wave functions solves the three-magnon problem for the S = 1 isotropic ferromagnetic infinite chain. The four-magnon problem is briefly discussed.

arXiv:1506.01554•Journal of Statistical Mechanics Theory and Experiment•Mar 1, 2016•7 citations

Introduction to the Bethe ansatz I

Michael Karbach, Gerhard H. Muller

The Bethe ansatz for the one-dimensional s=1/2 Heisenberg ferromagnet is introduced at an elementary level. The presentation follows Bethe's original work very closely. A detailed description and a complete classification of all two-magnon scattering states and two-magnon bound states are given for finite and infinite chains. The paper is designed as a tutorial for beginning graduate students. It includes 10 problems for further study.

arXiv:cond-mat/9809162•Sep 10, 1998•11 citations

Bethe ansatz for two-magnon scattering states in 2D and 3D Heisenberg–Ising ferromagnets †

P. N. Bibikov

Abstract Two different versions of Bethe ansatz are suggested for evaluation of scattering two-magnon states in 2D and 3D Heisenberg–Ising ferromagnets on square and simple cubic lattices. It is shown that the two-magnon sector is subdivided on two subsectors related to non-interacting and scattering magnons. The former subsector possess an integrable regular dynamics and may be described by a natural modification of the usual Bethe Ansatz. The latter one is characterized by a non-integrable chaotic dynamics and may be treated only within discrete degenerative version of Bethe Ansatz previously suggested by the author. Some of these results are generalized for multi-magnon states of the Heisenberg–Ising ferromagnet on a D dimensional hyper cubic lattice.

arXiv:1705.04117•Journal of Statistical Mechanics Theory and Experiment•Apr 1, 2018•4 citations

The Extended Bethe Ansatz for Infinite S = 1/2 Quantum Spin Chains with Non-Nearest-Neighbor Interaction

V. I. lnozemtsev

It is shown that the description of the states of infinite S = 1/2 interacting spin systems with the Hamiltonian H s J Z a2 sinh-Za(J / ) (~ 1) 2 j# t , j , l~Z 2 can be performed by studying the hyperbolic Calogero-Sutherland eigenvalue problem. The construction of multimagnon wave functions in each N-magnon sector is based on solutions of the set of linear algebraic equations which determine also the structure of zonal spherical functions on symmetric spaces X ~ = SL(N, H)/Sp(N) of negative curvature. The usual Bethe Ansatz for the XXX Heisenberg model corresponds to asymptotic forms of these wave functions at small values of a 1 or large distances between spins turned over the ferromagnetic ground state.

•Jan 1, 2005•0 citations

The extended Bethe Ansatz for infiniteS=1/2 quantum spin chains with non-nearest-neighbor interaction

V. I. Inozemtsev

Communications in Mathematical Physics•Aug 1, 1992•15 citations

Mixed-spin Ising model on the Bethe lattice

N. R. da Silva, Silvio R. A. Salinas

We obtain the phase diagram of a ferromagnetic mixed Ising system, consisting of spin-1/2 and spin-S variables, on a Bethe lattice of coordination number z, with nearest-neighbor exchange interactions and single-ion terms. The problem is formulated as a discrete nonlinear map. There is a tricritical point for S integer and z\ensuremath{\ge}5. In the infinite-coordination-number limit, we regain the results of an exact calculation for a Curie-Weiss version of the model.

Physical review. B, Condensed matter•Jul 1, 1991•57 citations
Bethe Ansatz approach to the three-magnon problem in an infinite XXXXXX spin chain with Izing next neighboring ferromagnetic interaction
Using the traditional and degenerative discrete-diffractive versions of Bethe Ansatz we construct a rude set of three-magnon states in the infinite XXXXXX spin chain with Izing next neighboring ferromagnetic term.
Abstract Two different versions of Bethe ansatz are suggested for evaluation of scattering two-magnon states in 2D and 3D Heisenberg–Ising ferromagnets on square and simple cubic lattices. It is shown that the two-magnon sector is subdivided on two subsectors related to non-interacting and scattering magnons. The former subsector possess an integrable regular dynamics and may be described by a natural modification of the usual Bethe Ansatz. The latter one is characterized by a non-integrable chaotic dynamics and may be treated only within discrete degenerative version of Bethe Ansatz previously suggested by the author. Some of these results are generalized for multi-magnon states of the Heisenberg–Ising ferromagnet on a D dimensional hyper cubic lattice.
It is shown that the description of the states of infinite S = 1/2 interacting spin systems with the Hamiltonian H s J Z a2 sinh-Za(J / ) (~ 1) 2 j# t , j , l~Z 2 can be performed by studying the hyperbolic Calogero-Sutherland eigenvalue problem. The construction of multimagnon wave functions in each N-magnon sector is based on solutions of the set of linear algebraic equations which determine also the structure of zonal spherical functions on symmetric spaces X ~ = SL(N, H)/Sp(N) of negative curvature. The usual Bethe Ansatz for the XXX Heisenberg model corresponds to asymptotic forms of these wave functions at small values of a 1 or large distances between spins turned over the ferromagnetic ground state.