Spectral functions of the J₁-J₂ Heisenberg model on the triangular lattice

Quantum spin liquids (QSL) are exotic states that host fractionalized excitations, such as magnetic monopoles, spinons, and anyons. In fact, anyons are quasiparticles that fall outside of the boson/fermion dichotomy and promise a fault-tolerant means to perform quantum computation and other quantum information processing. Such QSL states naturally arise in frustrated magnetic systems, such as the J₁-J₂ Heisenberg model on the triangular lattice. However, smoking-gun signals for quantum spin liquid states are still difficult to identify, both theoretically and experimentally. One promising pathway to identify QSL signatures is by looking at the dynamical structure factor spectral function, relevant for neutron scattering experiments, as this quantity probes the spin excitations directly. Calculating the dynamical structure factor for two-dimensional frustrated spin systems has been unobtainable until very recent advancements in matrix product state (MPS) simulations. In this work, we use MPS to calculate the dynamical structure factor for the J₁-J₂ Heisenberg model on the triangular lattice, across the full phase diagram. We identify signatures in the low-energy spectrum that distinguish the gapped Z₂, U(1) Dirac, and spinon Fermi surface QSL states. Then by examining the low-energy spectrum as we tune the Hamiltonian through the phase transition into the QSL phase, we find gapless modes at the corner (K) and center (M) of the Brillouin zone boundary, implying a U(1) Dirac spin liquid ground state. We discuss the implications of our work on prior and future neutron scattering experiments in triangular lattice compounds.