The existence of a gapped chiral spin liquid has been recently suggested in the vicinity of the metal-insulator transition of the Hubbard model on the triangular lattice, by intensive density-matrix renormalization group (DMRG) simulations [A. Szasz, J. Motruk, M. P. Zaletel, and J. E. Moore, Phys. Rev. X 021042 (2020)]. Here, we report the results obtained within the variational Monte Carlo technique based upon Jastrow-Slater wave functions, implemented with backflow correlations. As in DMRG calculations, we consider N-leg cylinders. For N = 4 and in the presence of a next-nearest-neighbor hopping, a chiral spin liquid emerges between the metal and the insulator with magnetic quasi-long-range order. Within our approach, the chiral state is gapped and breaks the reflection symmetry. By contrast, for both N = 5 and 6, the chiral spin liquid is not the state with the lowest variational energy: in the former case, a nematic spin liquid is found in the entire insulating regime, while for the less frustrated case with N = 6 the results are very similar to that obtained on two-dimensional clusters [L. F. Tocchio, A. Montorsi, and F. Becca, Phys. Rev. B 102, 115150 (2020)], with an antiferromagnetic phase close to the metal-insulator transition and a nematic spin liquid in the strong-coupling regime.
