Revisiting magnon bound states: ferro-antiferromagnetic $J_1-J_2$ square-lattice model

Abstract

A comprehensive analysis of pairing and bound states of magnons in the Heisenberg $S=1/2$ square-lattice $J_1-J_2$ ferro-antiferromagnetic model is presented. We highlight the similarities and differences between the bound states of spin flips on a lattice and those of particles in the continuum. Magnon bound states at finite pair momentum are studied throughout the Brillouin zone and a convenient lattice partial-wave nomenclature is advocated. The mechanisms of enhanced stability or fragility of these bound states for the high-symmetry pair momenta are identified and quantified as relating to the effective dimensional reduction or enhancement, respectively. These effects are also shown to control the evolution of the bound states with the model parameters, providing a transparent framework for understanding magnon pairing in a more general setting. A method to determine the bound state phase boundaries is presented.

37 pages, 17 figures. Supplementary Material (SM) available under "Ancillary files"