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

Physical review. B, Condensed matter

Bethe ansatz for two-magnon bound states in anisotropic magnetic chains of arbitrary spin

N. Papanicolaou, G. C. Psaltakis

Published Jan 1, 1987• 37 citations
Publisher

Abstract

The two-magnon spectra in anisotropic magnetic chains of arbitrary spin are derived by an elementary method which is an extension of Bethe's original ansatz for spin-(1/2) systems. Applications are presented for quantum spin chains with uniaxial or Ising Anisotropy as well as chains with quartic exchange interactions. The nature of certain collective modes emerging in a 1/n expansion is also clarified.

DOI
10.1103/physrevb.35.342

Related papers

Multiple bound states in the spin-1/2chain with Ising/Heisenberg/XY exchange

R P Hodgson, John B. Parkinson

Bound states and multiple bound states are studied in a linear chain of N spin= 1 / 2 atoms with anisotropic exchange, using the Bethe method. Some analytic results are presented for the infinite chain together with a large number of numerical results for chains of eight and twelve atoms. The breakup of isolated bound states occurs by successively splitting off 'free' magnons as the anisotropy varies. Similar behaviour occurs with the multiple bound states although in one case a strong interaction between a bound state and a 'free' magnon was observed.

Journal of Physics C Solid State Physics•Jun 30, 1984•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-deviation states in quantum spin chains of arbitrary S with anisotropic Heisenberg exchange

R P Hodgson, John B. Parkinson

The Bethe ansatz is used to calculate the eigenstates of Heisenberg spin chains of arbitrary S with two deviations from the completely aligned state. The states are analysed into bound (class A/B) and 'free' (class C). States with a high probability of having two deviations on the same site are found to be class C. The authors also obtain asymptotic expressions for the magnetisation and the autocorrelation function in the spin-flop phase as the field approaches the spin-flop critical field.

Journal of Physics C Solid State Physics•Dec 10, 1985•30 citations

Two-magnon excitations in quantum spin chains

Jianmin Liu, Jill C. Bonner

Quantum spin chains of higher spin are interesting in the case of both ferromagnets and antiferromagnets. They comprise a wide range of model types—Bethe–Ansatz integrable, nonintegrable, and with limited integrability. It is not well appreciated that the two-magnon (two-body) problems is always solvable, by Bethe–Ansatz and Green’s-function techniques, regardless of the integrability character of the entire model, with interesting implications in the context of solitons and bound solitons. Chubukov and Kveschenko have suggested using the two-magnon problem in a test for integrability and claim to find additional classes of integrable spin chains for s=1 and s= (3)/(2) . Here we investigate this situation.

Journal of Applied Physics•Apr 15, 1988•4 citations

Ground state and low excitations of an integrable chain with alternating spins

St Meiß ner, B-D Dörfel

An anisotropic integrable spin chain, consisting of spins s = 1 and , is investigated [1]. It is characterized by two real parameters and , the coupling constants of the spin interactions. For the case and the ground-state configuration is obtained by means of thermodynamic Bethe ansatz. Furthermore, the low excitations are calculated. It turns out that apart from free magnon states being the holes in the ground-state rapidity distribution, there exist bound states given by special string solutions of Bethe ansatz equations (BAE) in analogy to [13]. The dispersion law of these excitations is calculated numerically.

arXiv:hep-th/9605040•Journal of Physics A Mathematical and General•May 7, 1996•9 citations

Ground state and low excitations of an integrable chain with alternating spins

Meissner, S, B -D Dorfel

An anisotropic integrable spin chain, consisting of spins $s=1$ and $s=\frac{1}{2}$, is investigated \cite{devega}. It is characterized by two real parameters $\bar{c}$ and $\tilde{c}$, the coupling constants of the spin interactions. For the case $\bar{c}<0$ and $\tilde{c}<0$ the ground state configuration is obtained by means of thermodynamic Bethe ansatz. Furthermore the low excitations are calculated. It turns out, that apart from free magnon states being the holes in the ground state rapidity distribution, there exist bound states given by special string solutions of Bethe ansatz equations (BAE) in analogy to \cite{babelon}. The dispersion law of these excitations is calculated numerically.

•Jan 1, 1995•6 citations
The two-magnon spectra in anisotropic magnetic chains of arbitrary spin are derived by an elementary method which is an extension of Bethe's original ansatz for spin-(1/2) systems. Applications are presented for quantum spin chains with uniaxial or Ising Anisotropy as well as chains with quartic exchange interactions. The nature of certain collective modes emerging in a 1/n expansion is also clarified.
Bound states and multiple bound states are studied in a linear chain of N spin= 1 / 2 atoms with anisotropic exchange, using the Bethe method. Some analytic results are presented for the infinite chain together with a large number of numerical results for chains of eight and twelve atoms. The breakup of isolated bound states occurs by successively splitting off 'free' magnons as the anisotropy varies. Similar behaviour occurs with the multiple bound states although in one case a strong interaction between a bound state and a 'free' magnon was observed.
The Bethe ansatz is used to calculate the eigenstates of Heisenberg spin chains of arbitrary S with two deviations from the completely aligned state. The states are analysed into bound (class A/B) and 'free' (class C). States with a high probability of having two deviations on the same site are found to be class C. The authors also obtain asymptotic expressions for the magnetisation and the autocorrelation function in the spin-flop phase as the field approaches the spin-flop critical field.
Quantum spin chains of higher spin are interesting in the case of both ferromagnets and antiferromagnets. They comprise a wide range of model types—Bethe–Ansatz integrable, nonintegrable, and with limited integrability. It is not well appreciated that the two-magnon (two-body) problems is always solvable, by Bethe–Ansatz and Green’s-function techniques, regardless of the integrability character of the entire model, with interesting implications in the context of solitons and bound solitons. Chubukov and Kveschenko have suggested using the two-magnon problem in a test for integrability and claim to find additional classes of integrable spin chains for s=1 and s= (3)/(2) . Here we investigate this situation.
An anisotropic integrable spin chain, consisting of spins s = 1 and , is investigated [1]. It is characterized by two real parameters and , the coupling constants of the spin interactions. For the case and the ground-state configuration is obtained by means of thermodynamic Bethe ansatz. Furthermore, the low excitations are calculated. It turns out that apart from free magnon states being the holes in the ground-state rapidity distribution, there exist bound states given by special string solutions of Bethe ansatz equations (BAE) in analogy to [13]. The dispersion law of these excitations is calculated numerically.
An anisotropic integrable spin chain, consisting of spins s=1s=1s=1 and s=12s=\frac{1}{2}s=21​, is investigated \cite{devega}. It is characterized by two real parameters cˉ\bar{c}cˉ and c~\tilde{c}c~, the coupling constants of the spin interactions. For the case cˉ<0\bar{c}<0cˉ<0 and c~<0\tilde{c}<0c~<0 the ground state configuration is obtained by means of thermodynamic Bethe ansatz. Furthermore the low excitations are calculated. It turns out, that apart from free magnon states being the holes in the ground state rapidity distribution, there exist bound states given by special string solutions of Bethe ansatz equations (BAE) in analogy to \cite{babelon}. The dispersion law of these excitations is calculated numerically.