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

KAMIYA, YOSHITOMO; BATISTA, C.D.; ZHANG, SHANG-SHUN; MANUEL, L.O.; GHIOLDI, E.A.; TRUMPER, A.E.

PHYSICAL REVIEW B

AMER PHYSICAL SOC

Lugar: New York; Año: 2019 vol. 100 p. 104431 - 104431

1098-0121

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 correctsemiclassical behavior, large-N theories, on the other hand, emphasize the quantumness of spin fluctuations. In order to evaluate the possibility of the nontrivial recovery of the semiclassical magnetic excitations within a large-N approach, we compute the large-S limit of the dynamical spin structure factor of the triangular latticeHeisenberg 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 toexactly 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 random phase approximationpropagator. 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.