Large- S limit of the large- N theory for the triangular antiferromagnet

Abstract

Large-S and large-N theories (spin value S and spinor component number N ) are complementary, and sometimes conflicting, approaches to quantum magnetism. While large-S spin-wave theory captures the correct semiclassical behavior, large-N theories, on the other hand, emphasize the quantumness of spin fluctuations. In order to evaluate the possibility of the non-trivial recovery of the semiclassical magnetic excitations within a large-N approach, we compute the large-S limit of the dynamic spin structure of the triangular lattice Heisenberg antiferromagnet within a Schwinger boson spin representation. We demonstrate that, only after the incorporation of Gaussian (1/N ) corrections to the saddle-point (N = ∞) approximation, we are able to exactly reproduce the linear spin wave theory results in the large-S limit. The key observation is that the effect of 1/N corrections is to cancel out exactly the main contribution of the saddle-point solution; while the collective modes (magnons) consist of two spinon bound states arising from the poles of the RPA propagator. This result implies that it is essential to consider the interaction of the spinons with the emergent gauge fields and that the magnon dispersion relation should not be identified with that of the saddle-point spinons. arXiv:1905.10689v1 [cond-mat.str-el]

Avoided quasiparticle decay and enhanced excitation continuum in the spin- 12 near-Heisenberg triangular antiferromagnet Ba3CoSb2O9

“…Another important unresolved aspect is the nature of the high-energy excitations beyond one-magnon energies and to what extent those could be captured quantitatively by two-magnon excitations within a spin-wave expansion. Alternative approaches propose instead that the higher-energy continuum excitations are better understood in terms of pairs of unbound spin- 1 2 spinons [20,21], with the magnons at low energies corresponding to twospinon bound states [19,22,23].…”

Decay and renormalization of a longitudinal mode in a quasi-two-dimensional antiferromagnet

“…We note that the SU(3) Schwinger boson representation of the spin operators should not be confused with the Schwinger boson approximation (40)(41)(42)(43), which is qualitatively different from the semi-classical approach that we describe below. The magnetically ordered state of Ba2FeSi2O7 can be approximated by a product (mean-field) state of normalized SU(3) coherent states…”

Effectiveness of the Self-Consistent Harmonic Approximation in ferromagnets with dipolar interactions

“…On the other hand, phases with intact symmetry are better described by using the Schwinger bosonic representation [2][3][4][5], although three-dimensional models require special attention close to the transition temperature [6]. In general, the mean-field approach of the Schwinger formalism is sufficient for most of the scenarios; however, in frustrated models, the inclusion of Gaussian fluctuations should be considered [7][8][9][10], providing some extra complexity to the model. Moreover, it is also possible to represent the spin field by the non-linear sigma model O(3) [2,11,12] and then quantize the field fluctuations by standard techniques of quantum field theory (furthermore, note that in the AFM case, one should be careful with the topological phase).…”