Dynamical Structure Factor of the J1−J2 Heisenberg Model on the Triangular Lattice: Magnons, Spinons, and Gauge Fields - Ferrari, Francesco; Federico Becca (Physical review. X, 2019)
Understanding the nature of the excitation spectrum in quantum spin liquids is of fundamental importance, in particular for the experimental detection of candidate materials. However, current theoretical and numerical techniques have limited capabilities, especially in obtaining the dynamical structure factor, which gives a crucial characterization of the ultimate nature of the quantum state and may be directly assessed by inelastic neutron scattering. In this work, we investigate the low-energy properties of theS=1/2Heisenberg model on the triangular lattice, including both nearest-neighborJ1and next-nearest-neighborJ2superexchanges, by a dynamical variational Monte Carlo approach that allows accurate results on spin models. ForJ2=0, our calculations are compatible with the existence of a well-defined magnon in the whole Brillouin zone, with gapless excitations atKpoints (i.e., at the corners of the Brillouin zone). The strong renormalization of the magnon branch (also including rotonlike minima around theMpoints, i.e., midpoints of the border zone) is described by our Gutzwiller-projected state, where Abrikosov fermions are subject to a nontrivial magneticπflux threading half of the triangular plaquettes. When increasing the frustrating ratioJ2/J1, we detect a progressive softening of the magnon branch atM, which eventually becomes gapless within the spin-liquid phase. This feature is captured by the band structure of the unprojected wave function (with two Dirac points for each spin component). In addition, we observe an intense signal at low energies around theKpoints, which cannot be understood within the unprojected picture and emerges only when the Gutzwiller projection is considered, suggesting the relevance of gauge fields for the low-energy physics of spin liquids.