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

Journal of Physics C Solid State Physics

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

R P Hodgson, John B. Parkinson

Published Jun 30, 1984• 7 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3719/17/18/014

Related papers

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

N. Papanicolaou, G. C. Psaltakis

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.

Physical review. B, Condensed matter•Jan 1, 1987•37 citations

Two-Magnon Bound States in a Linear Heisenberg Chain with Nearest and Next Nearest Neighbor Interactions

Ikuo Ono, Syogo Mikado, Takehiko Oguchi

The bound state problems associated with two magnons in a linear chain of spin 1/2 with nearest and next nearest neighbor exchange integrals, J and α J , respectively, are studied. The Hamiltonian is rewritten in terms of the Fermi operators in place of spin operators, and an integral equation to determine the bound state energies is obtained. In the cases when the total wave number K of two magnons is π or π/2, analytical solutions are easily obtained. A part of the present results disagrees with Majumdar's ones. Computer studies on the bound states are performed for a finite chain composed of spins up to twenty. They are consistent with the analytical results.

Journal of the Physical Society of Japan•Feb 1, 1971•30 citations

The energy spectrum of a spin-1/2 ladder with mixed interactions

Vladyslav O. Cheranovskii, E. V. Ezerskaya, İlker Özkan

We studied the energy spectrum of two coupled XY spin-1/2 chains with different exchange integrals and inter-chain interaction of Ising type. The thorough analytical treatment of two-magnon states was given for finite and infinite lattice strips. To study the case of macroscopic number of inverted spins we used the corresponding density matrix renormalization group (DMRG) simulation. We also derived the self-consistent Bardeen-Cooper-Schrieffer (BCS) estimates for the lowest energies of the system. The comparison of the BCS and the DMRG estimates has shown incorrect behaviour of the BCS approximation for energy as a function of the intra-chain exchange integrals. To use the analytical results for two-magnon bound states we proposed a simple approximate formula for the lowest n -magnon energies of an infinite ladder with a more correct dependence on model parameters.

Journal of Physics Condensed Matter•May 4, 2001•3 citations

Multiple bound states in the quantum spin-1/2Heisenberg chain

R P Hodgson, John B. Parkinson

The Bethe method is used to analyse all the states of short chains of 8 and 12 atoms. The wavefunction of an isolated cluster of r deviations in an infinite chain is first expressed in the Bethe form. It is then possible to identify such clusters with reasonable confidence in short chains. In particular all the states that are not of class C have been classified in terms of multiple clusters.

Journal of Physics C Solid State Physics•Mar 10, 1983•3 citations

Multi-magnon excitations in Heisenberg spin-Schains with next-nearest-neighbour interactions

S L M Cyr, B. W. Southern, David A. Lavis

The spectra of both two- and three-magnon excitations in Heisenberg spin chains with next-nearest-neighbour (NNN) interactions are studied using scaling methods and the recursion method respectively. Both two-spin and three-spin couplings are considered for general spin S. In the three-magnon case, the asymptotic behaviour of the recursion coefficients can be used to directly identify the presence of bound states in the spectrum. Both integrable and non-integrable models can be studied, and the integrable models display special features in the bound-state spectra. Our results for the three-magnon bound states of S = 1 chains differ appreciably from those obtained in previous studies based upon an integral equation approach.

Journal of Physics Condensed Matter•Jun 24, 1996•4 citations

Heisenberg XXZ model and quantum Galilei group

F Bonechi, E Celeghini, R Giachetti +2 more

The 1D Heisenberg spin model with an anisotropy of the XXZ type is analysed in terms of the symmetry given by the quantum Galilei group Gamma q (1). For a chain with an infinite number of sites the authors show that the magnon excitations and the s=1/2, n-magnon bound states are determined by the algebra. In this case the Gamma q (1) symmetry provides a description naturally compatible with the Bethe ansatz. The recurrence relations determined by Gamma q (1) permit one to express the energy of the n-magnon bound states in a closed form in terms of Tchebischeff polynomials.

arXiv:hep-th/9204054•Journal of Physics A Mathematical and General•Aug 7, 1992•46 citations
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 bound state problems associated with two magnons in a linear chain of spin 1/2 with nearest and next nearest neighbor exchange integrals, J and α J , respectively, are studied. The Hamiltonian is rewritten in terms of the Fermi operators in place of spin operators, and an integral equation to determine the bound state energies is obtained. In the cases when the total wave number K of two magnons is π or π/2, analytical solutions are easily obtained. A part of the present results disagrees with Majumdar's ones. Computer studies on the bound states are performed for a finite chain composed of spins up to twenty. They are consistent with the analytical results.
We studied the energy spectrum of two coupled XY spin-1/2 chains with different exchange integrals and inter-chain interaction of Ising type. The thorough analytical treatment of two-magnon states was given for finite and infinite lattice strips. To study the case of macroscopic number of inverted spins we used the corresponding density matrix renormalization group (DMRG) simulation. We also derived the self-consistent Bardeen-Cooper-Schrieffer (BCS) estimates for the lowest energies of the system. The comparison of the BCS and the DMRG estimates has shown incorrect behaviour of the BCS approximation for energy as a function of the intra-chain exchange integrals. To use the analytical results for two-magnon bound states we proposed a simple approximate formula for the lowest n -magnon energies of an infinite ladder with a more correct dependence on model parameters.
The spectra of both two- and three-magnon excitations in Heisenberg spin chains with next-nearest-neighbour (NNN) interactions are studied using scaling methods and the recursion method respectively. Both two-spin and three-spin couplings are considered for general spin S. In the three-magnon case, the asymptotic behaviour of the recursion coefficients can be used to directly identify the presence of bound states in the spectrum. Both integrable and non-integrable models can be studied, and the integrable models display special features in the bound-state spectra. Our results for the three-magnon bound states of S = 1 chains differ appreciably from those obtained in previous studies based upon an integral equation approach.
The 1D Heisenberg spin model with an anisotropy of the XXZ type is analysed in terms of the symmetry given by the quantum Galilei group Gamma q (1). For a chain with an infinite number of sites the authors show that the magnon excitations and the s=1/2, n-magnon bound states are determined by the algebra. In this case the Gamma q (1) symmetry provides a description naturally compatible with the Bethe ansatz. The recurrence relations determined by Gamma q (1) permit one to express the energy of the n-magnon bound states in a closed form in terms of Tchebischeff polynomials.