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We analyze a recently proposed method to create fractional quantum Hall (FQH) states of atoms confined in optical lattices [A. S{\o}rensen {\it et al.}, Phys. Rev. Lett. {\bf 94} 086803 (2005)]. Extending the previous work, we investigate…

The experimental discovery of fractional quantum anomalous Hall (FQAH) states in tunable moir\'e superlattices has sparked intense interest in exploring the interplay between topological order and symmetry breaking phases. In this paper, we…

We study ultracold Rydberg-dressed Bose gases subject to artificial gauge fields in the fractional quantum Hall (FQH) regime. The characteristics of the Rydberg interaction gives rise to interesting many-body ground states different from…

Fractional quantum anomalous Hall (FQAH) effect, a lattice analogue of fractional quantum Hall effect, offers a unique pathway toward fault-tolerant quantum computation and deep insights into the interplay of topology and strong…

Fractional quantum Hall (FQH) states, known for their robust topological order and the emergence of non-Abelian anyons, have captured significant interest due to the appealing applications in fault-tolerant quantum computing. Bottom-up…

Strongly interacting topological matter exhibits fundamentally new phenomena with potential applications in quantum information technology. Emblematic instances are fractional quantum Hall states, where the interplay of magnetic fields and…

The standard theoretical framework for fractional quantum anomalous Hall effect (FQAH) assumes an isolated flat Chern band in the single particle level. In this paper we challenges this paradigm for the FQAH recently observed in the…

In the search of fractional quantum anomalous Hall (FQAH) effect, the conventional wisdom is to start from a flat Chern band isolated from the rest of the Hilbert space by band gaps, so that many-body interaction can be projected to a…

We propose a scheme to realize the fractional quantum Hall system with atoms confined in a two-dimensional array of coupled cavities. Our scheme is based on simple optical manipulation of atomic internal states and inter-cavity hopping of…

Among the extensive studies of fractional quantum anomalous Hall (FQAH) states, there recently appears a growing interest in the topological states with coexisting charge density wave (CDW) orders. Such states are referred to as Hall…

We investigate the fractional quantum anomalous Hall (FQAH) effect in rhombohedral multilayer graphene (RnG) in the presence of a strong applied displacement field. We first introduce the interacting model of RnG, which includes the…

Remarkable recent experiments on the moir\'e structure formed by pentalayer rhombohedral graphene aligned with a hexagonal Boron-Nitride substrate report the discovery of a zero field fractional quantum hall effect. These "(Fractional)…

The interplay between spontaneous symmetry breaking and topology can result in exotic quantum states of matter. A celebrated example is the quantum anomalous Hall (QAH) state, which exhibits an integer quantum Hall effect at zero magnetic…

Rydberg atoms with dipole-dipole interactions provide intriguing platforms to explore exotic quantum many-body physics. Here we propose a novel scheme with laser-assisted dipole-dipole interactions to realize synthetic magnetic field for…

An exciting new prospect in condensed matter physics is the possibility of realizing fractional quantum Hall (FQH) states in simple lattice models without a large external magnetic field. A fundamental question is whether qualitatively new…

We consider a coupled system of Dirac operators that models spin- and valley-polarized gated rhombohedral graphene (RHG) with an arbitrary number of layers. We classify all quantum anomalous Hall phases that are compatible with the model…

We study fermions and hardcore bosons with long range dipolar interactions at fractional fillings in a topological checkerboard lattice with short-range hoppings up to next-next-nearest neighbors \cite{Neupert2011}. We consider the case…

The fractional quantum anomalous Hall effect (FQAHE), the analog of the fractional quantum Hall effect1 at zero magnetic field, is predicted to exist in topological flat bands under spontaneous time-reversal-symmetry breaking. The…

Recent proposals of topological flat band (TFB) models have provided a new route to realize the fractional quantum Hall effect (FQHE) without Landau levels. We study hard-core bosons with short-range interactions in two representative TFB…

The fractional quantum Hall (FQH) effect arises from strong electron correlations in a quantising magnetic field, and features exotic emergent phenomena such as electron fractionalisation. Using the diagrammatic Monte Carlo approach with…