We study the effective dynamics of ferromagnetic spin chains in presence of long-range interactions. We consider the Heisenberg Hamiltonian in one dimension for which the spins are coupled through power-law long-range exchange interactions with exponent alpha. We add to the Hamiltonian an anisotropy in the z-direction. In the framework of a semiclassical approach, we use the Holstein-Primakoff transformation to derive an effective long-range discrete nonlinear Schrodinger equation. We then perform the continuum limit and we obtain a fractional nonlinear Schrodinger-like equation. Finally, we study the modulational instability of plane-waves in the continuum limit and we prove that, at variance with the short-range case, plane waves are modulationally unstable for alpha < 3. We also study the dependence of the modulation instability growth rate and critical wave-number on the parameters of the Hamiltonian and on the exponent alpha.(c) 2022 Elsevier B.V. All rights reserved.

Fractional dynamics and modulational instability in long-range Heisenberg chains / Laetitia, My; Nguenang, Jp; Paglan, Pa; Dauxois, T; Trombettoni, A; Ruffo, S. - In: COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION. - ISSN 1007-5704. - 117:(2023), pp. 1-17. [10.1016/j.cnsns.2022.106917]

Fractional dynamics and modulational instability in long-range Heisenberg chains

Nguenang, JP;Trombettoni, A;Ruffo, S
2023-01-01

Abstract

We study the effective dynamics of ferromagnetic spin chains in presence of long-range interactions. We consider the Heisenberg Hamiltonian in one dimension for which the spins are coupled through power-law long-range exchange interactions with exponent alpha. We add to the Hamiltonian an anisotropy in the z-direction. In the framework of a semiclassical approach, we use the Holstein-Primakoff transformation to derive an effective long-range discrete nonlinear Schrodinger equation. We then perform the continuum limit and we obtain a fractional nonlinear Schrodinger-like equation. Finally, we study the modulational instability of plane-waves in the continuum limit and we prove that, at variance with the short-range case, plane waves are modulationally unstable for alpha < 3. We also study the dependence of the modulation instability growth rate and critical wave-number on the parameters of the Hamiltonian and on the exponent alpha.(c) 2022 Elsevier B.V. All rights reserved.
2023
117
1
17
106917
https://www.sciencedirect.com/science/article/abs/pii/S100757042200404X
Laetitia, My; Nguenang, Jp; Paglan, Pa; Dauxois, T; Trombettoni, A; Ruffo, S
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/132090
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