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Effective field theories that describes the dynamics of a conserved U(1) current in terms of "hydrodynamic" degrees of freedom of topological phases in condensed matter are discussed in general dimension $D=d+1$ using the functional…

Fractional Chern insulators arise in topologically nontrivial flat bands, characterized by an integer Chern number C that corresponds to the number of dissipationless edge states in the non-interacting regime. Higher Chern numbers can…

Recent discoveries of zero-field fractional Chern insulators in moir\'e materials have attracted intensive research interests. However, most current theoretical and experimental attempts focus on systems with low Chern number bands, in…

We report the observation of a new series of Abelian and non-Abelian topological states in fractional Chern insulators (FCI). The states appear at bosonic filling nu= k/(C+1) (k, C integers) in several lattice models, in fractionally filled…

Recent theoretical works 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…

We suggest a construction of a large class of topological states using an array of quantum wires. First, we show how to construct a Chern insulator using an array of alternating wires that contain electrons and holes, correlated with an…

We derive the macroscopic charge and current densities of a Chern insulator initially occupying its electronic ground state as it responds to a finite-frequency electric field; we use a previously developed formalism based on microscopic…

We construct an algebraic description for the ground state and for the static response of the quantum Hall plateaux with filling factor $\nu=N/(2N+1)$ in the large $N$ limit. By analyzing the algebra of the fluctuations of the shape of the…

We construct a two-band lattice model whose bands can carry the Chern numbers C=0,pm1,pm2. By means of numerical exact diagonalization, we show that the most favorable situation that selects fractional Chern insulators (FCIs) is not…

Fractional Chern insulators (FCIs) -- the lattice analog of fractional quantum Hall states -- form as fractionalized quasiparticles emerge in a partially-filled Chern band. This fractionalization is driven by the interplay of electronic…

We theoretically and numerically investigate Chern vector insulators and topological surface states in a three-dimensional lattice, based on phase-delayed temporal-periodic interactions within the tight-binding model. These Floquet…

The search for robust examples of the magnetic version of topological insulators, referred to as quantum anomalous Hall insulators or simply Chern insulators, so far lacks success. Our groups have explored two distinct possibilities based…

We investigate the problem of intertwined orders in fractional Chern insulators by considering lattice fractional quantum Hall (FQH) states arising from pairing of composite fermions in the square-lattice Hofstadter model. At certain…

2+1 dimensional topological insulator described by the Kane-Mele model in the presence of Rashba spin-orbit interaction is considered. The effective action of the external fields coupled to electromagnetic and spin degrees of freedom is…

Strongly correlated quantum systems can exhibit exotic behavior controlled by topology. We predict that the \nu=1/2 fractional Chern insulator arises naturally in a two-dimensional array of driven, dipolar-interacting spins. As a specific…

We perform an exact-diagonalization study of quasihole excitations for the two-component Halperin $(221)$ state in the lowest Landau level and for several $\nu=1/3$ bosonic fractional Chern insulators in topological flat bands with Chern…

The insertion of a local magnetic flux, as the one created by a thin solenoid, plays an important role in gedanken experiments of quantum Hall physics. By combining Floquet engineering of artificial magnetic fields with the ability of…

The possibility of realizing lattice analogs of fractional quantum Hall (FQH) states, so-called fractional Chern insulators (FCIs), in nearly flat topological (Chern) bands has attracted a lot of recent interest. Here, we make the…

We have studied the fractional quantum Hall states on the surface of a topological insulator thin film in an external magnetic field, where the Dirac fermion nature of the charge carriers have been experimentally established only recently.…

We investigate the fate of hardcore bosons in a Harper-Hofstadter model which was experimentally realized by Aidelsburger et al. [Nature Physics 11 , 162 (2015)] at half filling of the lowest band. We discuss the stability of an emergent…