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- $\left(J_1\right)$, next-nearest- $\left(J_2\right)$, and third-neighbor $\left(J_3\right)$ interactions by using the density-matrix renormalization group (DMRG) method. By combining parallel DMRG with $\mathrm{SU}\left(2\right)$ spin rotational symmetry, we are able to obtain accurate results on large cylinders with length up to $L_x=48$ and circumference $L_y=6–12$. Our results suggest that the QSL phase of the $J_1\text{−}{J}_2$ 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 $J_3$ 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.

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• Quantum spin liquid
• Strongly correlated systems
• Density matrix renormalization group