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.
Highlights
Quantum spin liquid phases are unconventional states of matter that have gained a lot of attention in the last decades due to their fascinating properties and possible future applications in quantum devices like quantum computers [1,2,3]
The first goal of the present paper is to extend this investigation to the case of purely real ring exchange, where we find in particular a previously unnoticed phase that breaks lattice-rotational symmetry, and a spontaneous time-reversal symmetry breaking chiral spin liquids (CSL)
We found that the J-K model hosts a spontaneous timereversal symmetry breaking CSL for intermediate values of
Summary
Quantum spin liquid phases are unconventional states of matter that have gained a lot of attention in the last decades due to their fascinating properties and possible future applications in quantum devices like quantum computers [1,2,3]. From a theoretical point of view, they are expected to emerge in strongly correlated systems, for instance in Mott insulating phases. The recent progress in experiments with ultracold atoms in optical lattices opens the exciting new possibility to simulate a broad variety of such quantum models [4]. The optical lattice allows one to adjust the lattice type as well as the interaction strength, which can be tuned sufficiently to reach the Mott phase [5,6,7]. The fundamental degrees of freedom can be adjusted by the choice of atom type.
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