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arXiv:1210.4338 · Physical Review Letters

Spontaneous Time-Reversal Symmetry Breaking for Spinless Fermions on a Triangular Lattice

O. Tieleman, Omjyoti Dutta, Maciej Lewenstein, André Eckardt

Published Feb 28, 2013• 14 citations
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Abstract

As a minimal fermionic model with kinetic frustration, we study a system of spinless fermions in the lowest band of a triangular lattice with nearest-neighbor repulsion. We find that the combination of interactions and kinetic frustration leads to spontaneous symmetry breaking in various ways. Time-reversal symmetry can be broken by two types of loop current patterns, a chiral one and one that breaks the translational lattice symmetry. Moreover, the translational symmetry can also be broken by a density wave forming a kagome pattern or by a Peierls-type trimerization characterized by enhanced correlations among the sites of certain triangular plaquettes (giving a plaquette-centered density wave). We map out the phase diagram as it results from leading-order Ginzburg-Landau mean-field theory. Several experimental realizations of the type of system under study are possible with ultracold atoms in optical lattices.

DOI
10.1103/physrevlett.110.096405

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As a minimal fermionic model with kinetic frustration, we study a system of spinless fermions in the lowest band of a triangular lattice with nearest-neighbor repulsion. We find that the combination of interactions and kinetic frustration leads to spontaneous symmetry breaking in various ways. Time-reversal symmetry can be broken by two types of loop current patterns, a chiral one and one that breaks the translational lattice symmetry. Moreover, the translational symmetry can also be broken by a density wave forming a kagome pattern or by a Peierls-type trimerization characterized by enhanced correlations among the sites of certain triangular plaquettes (giving a plaquette-centered density wave). We map out the phase diagram as it results from leading-order Ginzburg-Landau mean-field theory. Several experimental realizations of the type of system under study are possible with ultracold atoms in optical lattices.
We study fermions in a lattice, with on-site and nearest neighbor attractive interactions between two spin species. We consider two geometries: (1) both spins in a triangular lattice and (2) a mixed geometry with up spins in honeycomb and down spins in triangular lattices. We focus on the interplay between spin-population imbalance, on-site and valence bond pairing, and order parameter symmetry. The mixed geometry leads to a rich phase diagram of topologically nontrivial phases. In both geometries, we predict order parameters with simultaneous time-reversal and translational symmetry breaking.
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We study the superfluid and insulating phases of interacting bosons on the triangular lattice with an inverted dispersion, corresponding to frustrated hopping between sites. The resulting single-particle dispersion has multiple minima at nonzero wave vectors in momentum space, in contrast to the unique zero-wave-vector minimum of the unfrustrated problem. As a consequence, the superfluid phase is unstable against developing additional chiral order that breaks time-reversal (T\mathcal{T}T) and parity (P\mathcal{P}P) symmetries by forming a condensate at nonzero wave vector. We demonstrate that the loss of superfluidity can lead to an even more exotic phase, the chiral Mott insulator, with nontrivial current order that breaks T,P\mathcal{T},\mathcal{P}T,P. These results are obtained via variational estimates, as well as a combination of bosonization and density-matrix renormalization group of triangular ladders, which, taken together, permit a fairly complete characterization of the phase diagram. We discuss the relevance of these phases to optical lattice experiments, as well as signatures of chiral symmetry breaking in time-of-flight images.
We studied the superfluidity of strongly repulsive fermionic atoms in optical lattices. Atoms are paired through a correlated tunneling mechanism, which induces superfluidity when repulsive nearest-neighbor interactions are included in the Hubbard model. This paired superfluid is a metastable state, which persists for a long time as the pair-broken process is severely suppressed. The mean-field phase diagram and low-energy excitations are investigated in a square lattice system. Intriguingly, spontaneous superflows may appear in the ground state of a triangular optical lattice system due to antiferromagnetic frustration.
We predict the robust existence of a novel quantum orbital stripe order in the p-band Bose-Hubbard model of two-dimensional triangular optical lattices with cold bosonic atoms. An orbital angular momentum moment is formed on each site exhibiting a stripe order both in the superfluid and Mott-insulating phases. The stripe order spontaneously breaks time-reversal, lattice translation, and rotation symmetries. In addition, it induces staggered plaquette bond currents in the superfluid phase. Possible signatures of this stripe order in the time of flight experiment are discussed.
Contrary to canonical expectations we show that lattice translational symmetry breaking often accompanies uniformly ordered flux phases. We demonstrate this phenomena by studying a spinless-fermion model on a square latttice with nearest-neighbor repulsion. We find an array of flux patterns, as a function interaction strength and filling factor, that break time-reversal symmetry but may or may not preserve translational symmetry. A key finding is that the pattern of flux ordering does not uniquely determine the electronic properties. As such a class of new phases of matter are introduced that expand the candidate ground states in many body interacting systems.