Related papers: Generalized Pseudopotentials for the Anisotropic F…
The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. Here, we construct a new type of fractional quantum Hall system, which has the special property that it lives in…
Many fractional quantum Hall wave functions are known to be unique and highest-density zero modes of certain "pseudopotential" Hamiltonians. Examples include the Read-Rezayi series (in particular, the Laughlin, Moore-Read and Read-Rezayi…
The quantum anomalous Hall (QAH) effect, a condensed matter analog of the parity anomaly, is characterized by a quantized Hall conductivity in the absence of an external magnetic field. However, it has been recently shown that, even in the…
The fractional quantum Hall (FQH) effect is one of the most striking phenomena in condensed matter physics. It is described by a simple Laughlin wavefunction and has been thoroughly studied both theoretically and experimentally. In lattice…
Recent work has extended topological band theory to open, non-Hermitian Hamiltonians, yet little is understood about how non-Hermiticity alters the topological quantization of associated observables. We address this problem by studying the…
We motivate a close look on the usefulness of the Gaffnian and Haffnian quasihole manifold (null spaces of the respective model Hamiltonians) for well-known gapped fractional quantum Hall (FQH) phases. The conformal invariance of these…
The understanding of the Chern insulator and anomalous quantum Hall effect (AQHE) in terms of chiral edge states in confined systems is the first aim of the paper. The model we use consists in a diatomic square lattice with hopping to the…
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 pseudopotentials describing interaction of Laughlin quasielectrons (QE) and quasiholes (QH) in an infinite fractional quantum Hall system are studied. The QE and QH pseudopotentials are similar which suggests the (approximate)…
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 consider the quantum Hall effect (QHE) in a system of interacting electrons. Our formalism is valid for systems in the presence of an external magnetic field, as well as for systems with a nontrivial band topology. That is, the…
We consider the anisotropic effect in the quantum Hall systems by applying a confining potential that is not of parabolic type. This can be done by extending Susskind--Polychronakos's approach to involve the matrices of two coupled harmonic…
We study the phase transitions of bosonic $\nu=1/2$ fractional quantum Hall (FQH) effect in different topological lattice models under the interplay of onsite periodic potential and Hubbard repulsion. Through exact diagonalization and…
We develop a theory for the pseudorelativistic fractional quantum Hall effect in graphene, which is based on a multicomponent abelian Chern-Simons theory in the fermionic functional integral approach. Calculations are performed in the…
Topological insulators are bulk electronic insulators which possess symmetry protected gapless modes on their surfaces. Breaking the symmetries that underlie the gapless nature of the surface modes is predicted to give rise to exotic new…
We analytically compute the thermal Hall conductance (THC) of fractional quantum Hall droplets under realistic conditions that go beyond the idealized linear edge theory with conformal symmetry. Specifically, we consider finite-size effects…
We have analyzed the effects of the anisotropic energy bands of phosphorene on magnetoroton branches for electrons and holes in the two Landau levels close to the band edges. We have found that the fractional quantum Hall effect gap in the…
Many robust physical phenomena in quantum physics are based on topological invariants arising due to intriguing geometrical properties of quantum states. Prime examples are the integer and fractional quantum Hall effects that demonstrate…
We study the role of Zeeman effect in fractional quantum Hall effect (FQHE) on the surface of topological insulators (TIs). We show that the effective pseudopotentials of the Coulomb interaction are reformed due to Zeeman effect, which are…
We present here a complete microscopic theory of a family of neutral excitations in the fractional quantum Hall fluids, related to the geometric fluctuations of the quantum Hall ground states. Many of the physical properties of such…