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Nematic Liquid Crystals of Bosons in Kagome Lattices with Syn- thetic Gauge Fields GUANYU ZHU, JENS KOCH, Northwestern University, IVAR MARTIN, Argonne National Laboratory | We consider a family of interact- ing boson models based on a kagome lattice with local synthetic gauge

Guanyu Zhu

Published Jan 1, 2015• 0 citations

Abstract

ux, which can be realized in an optical lattice with ultra-cold atoms. Such models have a lowest at band in the single particle spectrum. The at band is spanned by eigenstates forming localized loops on the lattice, with the maximally compact loop states typically breaking the discrete rotational symmetry of the lattice. When populated by locally-interacting particles, the close packing of such maximally compact loop states leads to a nematic loop crystal ground state. We predict that increasing the lling beyond the close packing fraction leads to the formation of quantum liquid crystals including a nematic supersolid and a nematic superuid phase with broken lattice rotation and U(1) symmetry. We also show how the nematicity can be probed by time-of-ight

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ux, which can be realized in an optical lattice with ultra-cold atoms. Such models have a lowest at band in the single particle spectrum. The at band is spanned by eigenstates forming localized loops on the lattice, with the maximally compact loop states typically breaking the discrete rotational symmetry of the lattice. When populated by locally-interacting particles, the close packing of such maximally compact loop states leads to a nematic loop crystal ground state. We predict that increasing the lling beyond the close packing fraction leads to the formation of quantum liquid crystals including a nematic supersolid and a nematic superuid phase with broken lattice rotation and U(1) symmetry. We also show how the nematicity can be probed by time-of-ight

The problem of interacting bosons in frustrated lattices is an intricate one due to the absence of a unique minimum in the single-particle dispersion where macroscopic number of bosons can condense. Here, we consider a family of tight-binding models with macroscopically degenerate lowest energy bands, separated from other bands by a gap. We predict the formation of exotic states that spontaneously break rotational symmetry at relatively low filling. These states belong to three nematic phases: Wigner crystal, supersolid, and superfluid. The Wigner crystal phase is established exactly at low filling. Supersolid and superfluid phases, at larger filling, are obtained by making use of a projection onto the flat band, construction of an appropriate Wannier basis, and subsequent mean-field treatment. The nematic superfluid that we predict is uniform in real space but has an anisotropic momentum distribution, providing a novel scenario for Bose condensation with an additional nematic order. Our findings open up a promising direction of studying microscopic quantum liquid crystalline phases of bosons.

We consider hard-core bosons on the kagome lattice in the presence of short-range repulsive interactions and focus particularly on the filling factor

1/3

. In the strongly interacting limit, the low-energy excitations can be described by the quantum fully packed loop coverings on the triangular lattice. Using a combination of tensor product state based methods and exact diagonalization techniques, we show that the system has an extended

{\mathbb{Z}}_{2}

topological liquid phase as well as a latti ce nematic phase. The latter breaks lattice rotational symmetry. By tuning appropriate parameters in the model, we study the quantum phase transition between the topological and the symmetry broken phases. We construct the critical theory for this transition using a mapping to an Ising gauge theory that predicts the transition to belong to the

O(3)

universality class.

As in between liquid and crystal phases lies a nematic liquid crystal, which breaks rotation with preservation of translation symmetry, there is a nematic superfluid phase bridging a superfluid and a supersolid. The nematic order also emerges in interacting electrons and has been found to largely intertwine with multiorbital correlation in high-temperature superconductivity, where Ising nematicity arises from a four-fold rotation symmetry C_{4} broken down to C_{2}. Here, we report an observation of a three-state (Z_{3}) quantum nematic order, dubbed "Potts-nematicity", in a system of cold atoms loaded in an excited band of a hexagonal optical lattice described by an sp^{2}-orbital hybridized model. This Potts-nematic quantum state spontaneously breaks a three-fold rotation symmetry of the lattice, qualitatively distinct from the Ising nematicity. Our field theory analysis shows that the Potts-nematic order is stabilized by intricate renormalization effects enabled by strong interorbital mixing present in the hexagonal lattice. This discovery paves a way to investigate quantum vestigial orders in multiorbital atomic superfluids.