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arXiv · 1802.03179

Time-reversal symmetry breaking Abelian chiral spin liquid in Mott phases of three-component fermions on the triangular lattice

C. Boos·C. J. Ganahl·M. Lajkó·P. Nataf·A. M. Läuchli·K. Penc·K. P. Schmidt·F. Mila
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Abstract

We provide numerical evidence in favor of spontaneous chiral symmetry breaking and the concomitant appearance of an Abelian chiral spin liquid for three-component fermions on the triangular lattice described by an SU(3) symmetric Hubbard model with hopping amplitude $-t$ ($t>0$) and on-site interaction $U$. This chiral phase is stabilized in the Mott phase with one particle per site in the presence of a uniform $\pi$-flux per plaquette, and in the Mott phase with two particles per site without any flux. Our approach relies on effective spin models derived in the strong-coupling limit in powers of $t/U$ for general SU$(N)$ and arbitrary uniform charge flux per plaquette, which are subsequently studied using exact diagonalizations and variational Monte Carlo simulations for $N=3$, as well as exact diagonalizations of the SU($3$) Hubbard model on small clusters. Up to third order in $t/U$, and for the time-reversal symmetric cases (flux $0$ or $\pi$), the low-energy description is given by the $J$-$K$ model with Heisenberg coupling $J$ and real ring exchange $K$. The phase diagram in the full $J$-$K$ parameter range contains, apart from three already known, magnetically long-range ordered phases, two previously unreported phases: i) a lattice nematic phase breaking the lattice rotation symmetry and ii) a spontaneous time-reversal and parity symmetry breaking Abelian chiral spin liquid. For the Hubbard model, an investigation that includes higher-order itinerancy effects supports the presence of a phase transition inside the insulating region, occurring at $(t/U)_{\rm c}\approx 0.07$ [$(U/t)_{\rm c} \approx 13$] between the three-sublattice magnetically ordered phase at small $t/U$ and this Abelian chiral spin liquid.

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C. Boos, C. J. Ganahl, M. Lajkó, P. Nataf, A. M. Läuchli, K. Penc, K. P. Schmidt, F. Mila. 2018-02-09. Time-reversal symmetry breaking Abelian chiral spin liquid in Mott phases of three-component fermions on the triangular lattice. https://doi.org/10.1103/physrevresearch.2.023098

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