Spectral function of the J 1 − J 2 Heisenberg model on the triangular lattice

Spectral probes, such as neutron scattering, are crucial for characterizing excitations in quantum many-body systems and the properties of quantum materials. Among the most elusive phases of matter are quantum spin liquids, which have no long-range order even at zero temperature and host exotic fractionalized excitations with nontrivial statistics. These phases can occur in frustrated quantum magnets, such as the paradigmatic Heisenberg model with nearest- and next-nearest-neighbor exchange interactions on the triangular lattice, the so-called J1−J2 model. In this work, we compute the spectral function using large-scale matrix product state simulations across the three different phases of this model's phase diagram, including a quantum spin-liquid phase at intermediate J2/J1. Despite a plethora of theoretical and experimental studies, the exact nature of this phase is still contested, with the dominant candidates being a gapped Z2, a gapless U(1) Dirac, and a spinon Fermi surface quantum spin-liquid state. We find a V-shaped spectrum near the center of the Brillouin zone (Γ point), a key signature of a spinon Fermi surface, observed in prior neutron scattering experiments. However, we find a small gap near the Γ point, ruling out such a phase. Furthermore, we find localized gapless excitations at the corner of the Brillouin zone boundary (K point) and the middle of the edge of the Brillouin zone boundary (M point), ruling out the gapped Z2 spin-liquid phase. Our results imply that the intermediate spin-liquid phase is a gapless U(1) Dirac spin liquid, and provide clear signatures to detect this phase in future neutron scattering experiments.