The Hubbard model on triangular $N$-leg cylinders: chiral and non-chiral spin liquids

TL;DR

This study investigates the nature of spin liquids in the Hubbard model on triangular N-leg cylinders using variational Monte Carlo, revealing the emergence of gapped chiral spin liquids and nematic phases depending on the number of legs and frustration.

Contribution

It introduces a variational Monte Carlo approach with backflow correlations to analyze spin liquids in the Hubbard model on N-leg cylinders, providing new insights into their properties and phase transitions.

Findings

Gapped chiral spin liquid appears for N=4 with next-nearest neighbor hopping.

Nematic spin liquids dominate for N=5 and N=6 in the insulating regime.

Results align with previous DMRG studies and extend understanding of spin liquid phases.

Abstract

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 {\bf 10}, 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 $N=6$, 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 the one obtained on two-dimensional clusters [L.F. Tocchio, A. Montorsi, and F. Becca, Phys. Rev. B {\bf 102}, 115150 (2020)], with an antiferromagnetic phase close to the metal-insulator transition and a nematic spin liquid in the strong-coupling regime.