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Journal of Physics Condensed Matter

Three-magnon excitations in ferromagnetic spin-S chains

B. W. Southern, R J Lee, David A. Lavis

Published Nov 14, 1994• 12 citations
Publisher

Abstract

The nature of three-magnon excitations in general spin-S quantum spin chains is studied using the recursion method. The asymptotic behaviour of the recurrence coefficients can be used to identify the presence of bound states in the spectrum. Special features of integrable models are easily identified.
DOI
10.1088/0953-8984/6/46/024

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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.
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The nature of multimagnon excitations in alternating spin/bond ferromagnetic chains are studied using a combination of scaling methods and the recursion method. Two-magnon excitations for a Heisenberg chain with either alternating spin magnitudes, SSS and ${S}^{\ensuremath{'}},$ or alternating nearest-neighbor couplings, J1{J}_{1}J1​ and J2{J}_{2}J2​ can be studied using real-space rescaling techniques. These results are then used to investigate three-magnon excitations using the recursion method.