Recent theoretical papers have demonstrated the realization of fractional quantum anomalous Hall states (also called fractional Chern insulators) in topological flat band lattice models without an external magnetic field. Such newly proposed lattice systems play a vital role in obtaining a large class of fractional topological phases. Here we report the exact numerical studies of edge excitations for such systems in a disk geometry loaded with hard-core bosons, which will serve as a more viable experimental probe for such topologically ordered states. We find convincing numerical evidence of a series of edge excitations characterized by the chiral Luttinger liquid theory for the bosonic fractional Chern insulators in both the honeycomb disk Haldane model and the kagome-lattice disk model. We further verify these current-carrying chiral edge states by inserting a central flux to test their compressibility.
We study a model of hard-core bosons on the kagome lattice with short-range hopping
(t) and repulsive interactions
(V). This model directly maps onto an easy-axis
S=1∕2 XXZ model on the kagome lattice and is also related, at large
V∕t, to a quantum dimer model on the triangular lattice. Using quantum Monte Carlo numerics, we map out the phase diagram of this model at half-filling. At
T=0, we show that this model exhibits a superfluid phase at small
V∕t and an insulating phase at large
V∕t, separated by a continuous quantum phase transition at ${V}_{c}∕t\ensuremath{\approx}19.8$. The insulating phase at
T=0 appears to have no conventional broken symmetries, and is thus a uniform Mott insulator (a ``spin liquid'' in magnetic language). We characterize this insulating phase as a uniform
Z2 fractionalized insulator from the topological order in the ground state and estimate its vison gap. Consistent with this identification, there is no apparent thermal phase transition upon heating the insulator. The insulating phase instead smoothly crosses over into the high temperature paramagnet via an intermediate cooperative paramagnetic regime. We also study the superfluid-to-normal thermal transition for
V<Vc. We find that this is a Kosterlitz-Thouless transition at small
V∕t but changes to a first order transition for
V closer to
Vc. We argue that this first order thermal transition is consistent with the presence of a nearby
Z2 insulating ground state obtained from the superfluid ground state by condensing double vortices.
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.
We study a model of strongly interacting spinless fermions and hard-core bosons on an anisotropic kagome lattice near 2/3-filling. Our main focus lies on the strongly anisotropic case in which the nearest–neighbor repulsions V and V ' are large compared to the hopping amplitudes | t | and | t '|. When t = t ' = 0, the system has a charge ordered insulating ground state where the charges align in striped configurations. Doping one electron or hole into the ground state yields an anisotropic metal at V ' > V , where the particle fractionalizes along the V '-bonds while propagates along the V -bonds in a one–body like manner. The sixth order ring exchange processes around the hexagonal unit of the lattice play a crucial role in forming a bound state of fractional charges.
We study hard-core bosons on the honeycomb lattice in the presence of anisotropic nearest-neighbor repulsive interactions. Using a quantum Monte Carlo (QMC) technique, we extract the phase diagram of the model in terms of the filling and the anisotropy. At half-filling we find a dimer insulator phase near maximum anisotropy that is characterized by a finite topological entanglement entropy
ln(2)/2, indicative of a fractional quantum Hall state for bosons. We identify the presence of edge states and derive a QMC-based method to extract and verify their chirality. Remarkably, this phase arises in the absence of magnetic flux and without explicit lattice frustration.
Using auxiliary-field quantum Monte Carlo simulations, we study the zero-temperature attractive Hubbard model on the kagome lattice at various relevant electronic fillings. The low-energy physics at
2/3-density is influenced by the Dirac point at the Fermi energy, wherein we unveil a superfluid transition at a critical attractive interaction
Uc/t=−4.58(3), which belongs to the chiral-XY universality class. This U(1) symmetry-breaking is not accompanied by charge order, even for substantially large interaction strengths, in a regime where a description in terms of hardcore bosons becomes increasingly suitable. An investigation of the latter shows that charge ordering at
1/3-filling only occurs at interaction strengths much larger than those corresponding to the mapping to the original fermionic model. Additionally, for densities exhibiting van Hove singularities in the non-interacting density of states, our results show that any attractive interaction gives rise to superfluidity, yet again without charge ordering, contrary to recent studies employing mean-field theory.