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In the framework of Hofstadter`s approach we provide a detailed analysis of a realization of exotic topological states such as the Chern insulator with large Chern numbers. In a transverse homogeneous magnetic field a one-particle spectrum of fermions transforms to an intricate spectrum with a fine topological structure of the subbands. In a weak magnetic field $H$ for a rational magnetic flux, a topological phase with a large Chern number is realized near the half filling. There is an abnormal behavior of the Hall conductance ${sigma_{xy}simeq frac{e}{2 H}}$. At half-filling, the number of chiral Majorana fermion edge states increases sharply forming a new state, called the chiral Majorana fermion liquid.
We formulate a Chern-Simons composite fermion theory for Fractional Chern Insulators (FCIs), whereby bare fermions are mapped into composite fermions coupled to a lattice Chern-Simons gauge theory. We apply this construction to a Chern insulator mode
A sizable transverse thermoelectric coefficient N , large to the extent that it potentially serves applications, is predicted to arise, by means of first-principles calculations, in a Skyrmion crystal assumed on EuO monolayer where carrier electrons
We study the relation between Chern numbers and Quantum Phase Transitions (QPT) in the XY spin-chain model. By coupling the spin chain to a single spin, it is possible to study topological invariants associated to the coupling Hamiltonian. These inva
We present evidence of a direct, continuous quantum phase transition between a Bose superfluid and the $ u=1/2$ fractional Chern insulator in a microscopic lattice model. In the process, we develop a detailed field theoretic description of this trans
We study a generic model of a Chern insulator supplemented by a Hubbard interaction in arbitrary even dimension $D$ and demonstrate that the model remains well-defined and nontrivial in the $D to infty$ limit. Dynamical mean-field theory is applicabl