Kavli Affiliate: Joel E. Moore
| First 5 Authors: Nicholas E. Sherman, Maxime Dupont, Joel E. Moore, ,
| Summary:
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 non-trivial 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 $J_1-J_2$ 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 $J_2/J_1$. Despite a plethora of theoretical and
experimental studies, the exact nature of this phase is still contested, with
the dominant candidates being a gapped $mathbb{Z}_2$, 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 ($Gamma$ point), a key
signature of a spinon Fermi surface, observed in prior neutron scattering
experiments. However, we find a small gap near the $Gamma$ 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 $mathbb{Z}_2$ 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.
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