Nematic Liquid Crystals of Bosons in Kagome Lattices with Synthetic Gauge Fields

Guanyu Zhu, Jens Koch, Ivar Martin

Alexandru Petrescu, S. M. Girvin, Karyn Le Hur

Guanyu Zhu

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

Krishanu Roychowdhury, Subhro Bhattacharjee, Frank Pollmann

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.

Krishanu Roychowdhury, Subhro Bhattacharjee, Frank Pollmann

Tristan Lugan, Ludovic D. C. Jaubert, Arnaud Ralko

The authors have theoretically explored the quantum phase diagram of a spin-1/2 square-kagome antiferromagnet, by means of Schwinger bosons. The paper presents two incommensurate magnetic states and a gapped topological quantum spin liquid with a weak lattice nematicity breaking. They further show dynamical structure factors of the phases as possible signatures observable in inelastic neutron scattering