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.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.

arXiv:1505.05998Physical Review BAug 26, 201530 citations

Interaction-driven fractional quantum Hall state of hard-core bosons on kagome lattice at one-third filling

W. Zhu, Shou-Shu Gong, D. N. Sheng

There has been a growing interest in realizing topologically nontrivial states of matter in band insulators, where a quantum Hall effect can appear as an intrinsic property of the band structure. While ongoing progress is under way with a number of directions, the possibility of realizing novel interaction-generated topological phases, without the requirement of a nontrivial invariant encoded in single-particle wave function or band structure, can significantly extend the class of topological materials and is thus of great importance. Here, we show an interaction-driven topological phase emerging in an extended Bose-Hubbard model on a kagome lattice, where the noninteracting band structure is topological trivial with zero Berry curvature in the Brillouin zone. By means of an unbiased state-of-the-art density-matrix renormalization group technique, we identify that the ground state in a broad parameter region is equivalent to a bosonic fractional quantum Hall Laughlin state, based on the characterization of universal properties including ground-state degeneracy, edge excitations, and anyonic quasiparticle statistics. Our work paves a way to finding an interaction-induced topological phase at the phase boundary of conventionally ordered solid phases.There has been a growing interest in realizing topologically nontrivial states of matter in band insulators, where a quantum Hall effect can appear as an intrinsic property of the band structure. While ongoing progress is under way with a number of directions, the possibility of realizing novel interaction-generated topological phases, without the requirement of a nontrivial invariant encoded in single-particle wave function or band structure, can significantly extend the class of topological materials and is thus of great importance. Here, we show an interaction-driven topological phase emerging in an extended Bose-Hubbard model on a kagome lattice, where the noninteracting band structure is topological trivial with zero Berry curvature in the Brillouin zone. By means of an unbiased state-of-the-art density-matrix renormalization group technique, we identify that the ground state in a broad parameter region is equivalent to a bosonic fractional quantum Hall Laughlin state, based on the characterization of universal properties including ground-state degeneracy, edge excitations, and anyonic quasiparticle statistics. Our work paves a way to finding an interaction-induced topological phase at the phase boundary of conventionally ordered solid phases.

arXiv:1509.05509Physical review. B./Physical review. BJul 13, 201626 citations

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.