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We apply the magneto-roton theory of the fractional quantum Hall effect to study the collective excitation spectrum of rotating dipolar Fermi gases. The predicted spectrum has a finite energy gap in the long wavelength limit and a roton…
Collective excitations play a vital role in understanding the exotic phases of matter and phase transitions in quantum many-body systems. For the first time, we numerically (via exact diagonalization and density matrix renormalization…
In this paper we study the spectrum of low-energy edge excitations of a fractional quantum Hall (FQH) droplet. We show how to generate, by conformal field theory (CFT) techniques, the many-electron wave functions for the edge states. And we…
The low energy neutral excitations of incompressible fractional quantum Hall states are called collective modes or magnetic excitons. This work develops techniques for computing their dispersion at general filling fractions for reasonably…
Motivated by the quasiparticle wavefunction in the composite fermion (CF) theory for fractional quantum Hall filling factor $\nu = 1/m$, I consider a suitable quasiparticle operator in differential form, as a modified form of Laughlin's…
Rotationally invariant fractional quantum Hall (FQH) states have long been understood in terms of composite bosons or composite fermions. Recent investigations of both incompressible and compressible states in highly tilted fields, which…
We develop a general algebraic scheme to decompose fractional quantum Hall (FQH) wave functions based on the operator contraction multiplication. By introducing fermionic and bosonic operators and establishing three fundamental contraction…
We show a generic formation of the primary magnetorotons in the collective modes of the observed "unconventional" fractional quantum Hall effect (FQHE) states of the composite fermions at the filling factors 4/11, 4/13, 5/13, 5/17, and 3/8…
The fractional quantum Hall effect (FQHE) is a canonical example of a topological phase in a correlated 2D electron gas under strong magnetic field. While electric currents propagate as chiral downstream edge modes, chargeless upstream…
The fractional quantum Hall effect (FQHE) observed at half filling of the second Landau level is believed to be caused by a pairing of composite fermions captured by the Moore-Read Pfaffian wave function. The generating Hamiltonian for the…
We propose a systematical approach to construct generic fractional quantum anomalous Hall (FQAH) states, which are generalizations of the fractional quantum Hall states to lattice models with zero net magnetic field and full lattice…
We present a comprehensive numerical study of a microscopic model of the fractional quantum Hall system at filling fraction $\nu = 5/2$, based on the disc geometry. Our model includes Coulomb interaction and a semi-realistic confining…
The Kohn-Sham density functional method for the fractional quantum Hall (FQH) effect has recently been developed by mapping the strongly interacting electrons into an auxiliary system of weakly interacting composite fermions (CFs) that…
We use the dynamical structure factors of the quantum Hall states at $\nu=1/3$ and $\nu=1/2$ in the lowest Landau level to study their excitation spectrum. Using the density matrix renormalization group in combination with the…
We investigate the 1/3 fractional quantum Hall state with one and two quasiparticle excitations. It is shown that the quasiparticle excitations are best described as excited composite fermions occupying higher composite-fermion quasi-Landau…
The neutral fermionic edge mode is essential to the non-Abelian topological property and its experimental detection in $Z_k$ fractional quantum Hall (FQH) state for $k > 1$. Usually, the identification of the edge modes in a finite size…
The construction of fractional quantum Hall (FQH) states from the two-dimensional array of quantum wires provides a useful way to control strong interactions in microscopic models and has been successfully applied to the Laughlin,…
Quantum gases are used to simulate the physics of the lowest Landau level (LLL) with neutral atoms, which in the simplest setup is achieved by rotating the gas at the confining harmonic trap frequency, a requirement that is difficult to…
Matrix product state techniques provide a very efficient way to numerically evaluate certain classes of quantum Hall wave functions that can be written as correlators in two-dimensional conformal field theories. Important examples are the…
In a twisted graphene on hexagonal Boron Nitride, the presence of a gap and the breaking of the symmetry between carbon sublattices leads to multicomponent fractional quantum Hall effect (FQHE) due to the electrons correlation. We report on…