Kernel Polynomial Method for Linear Spin Wave Theory

Abstract

Calculating dynamical spin correlations is essential for matching model magnetic exchange Hamiltonians to momentum-resolved spectroscopic measurements. A major numerical bottleneck is the diagonalization of the dynamical matrix, especially in systems with large magnetic unit cells, such as those with incommensurate magnetic structures or quenched disorder. In this paper, we demonstrate an efficient scheme based on the kernel polynomial method for calculating dynamical correlations of relevance to inelastic neutron scattering experiments. This method reduces the scaling of numerical cost from cubic to linear in the magnetic unit cell size.

Submission to SciPost. 27 pages, 6 figures. Typos corrected, added additional minor comments to derivations

References in corpus (17)

• Advances in the Physics of Magnetic Skyrmions and Perspective for Technology
• The Kernel Polynomial Method
• Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4
• Skyrmions and Anomalous Hall Effect in a Dzyloshinskii-Moriya Spiral Magnet
• Hyper-honeycomb iridate $\beta$-Li2IrO3 as a platform for Kitaev magnetism
• Spontaneous Magnon Decays
• Crystalline Electric Field Randomness in the Triangular Lattice Spin-Liquid YbMgGaO${}_4$
• Evidence of Flat Bands and Correlated States in Buckled Graphene Superlattices
• Anomalous High-Energy Spin Excitations in La2CuO4
• Physical realization of a quantum spin liquid based on a novel frustration mechanism
• Non-coplanar and counter-rotating incommensurate magnetic order stabilized by Kitaev interactions in $\gamma$-Li2IrO3
• Unconventional magnetic order on the hyperhoneycomb Kitaev lattice in $\beta$-Li2IrO3: full solution via magnetic resonant x-ray diffraction
• Vacancy defects and monopole dynamics in oxygen-deficient pyrochlores
• Classical spin dynamics based on SU($N$) coherent states
• Order from structural disorder in $XY$ pyrochlore antiferromagnet $\mathrm{E}{\mathrm{r}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$
• Impurity-induced frustration in correlated oxides
• From one- to two-magnon excitations in the S=3/2 magnet $\beta$-CaCr${}_2$O${}_4$

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