Nature of quantum spin liquids of the S=21 Heisenberg antiferromagnet on the triangular lattice: A parallel DMRG study

We study the ground-state properties of the quantum spin liquid (QSL) phases of the spin-1/2 antiferromagnetic Heisenberg model on the triangular lattice with nearest- (J1), next-nearest- (J2), and third-neighbor (J3) interactions by using the density-matrix renormalization group (DMRG) method. By combining parallel DMRG with SU(2) spin rotational symmetry, we are able to obtain accurate results on large cylinders with length up to Lx = 48 and circumference Ly = 6-12. Our results suggest that the QSL phase of the J1-J2 Heisenberg model is gapped, which is characterized by the absence of a gapless mode and by short-range spin-spin and dimer-dimer correlations. In the presence of J3 interaction, we find that a critical QSL with a single gapless mode emerges. While both spin-spin and scalar chiral-chiral correlations are short ranged, dimer-dimer correlations are quasi long ranged and decay as a power law at long distances.