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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 consider a disordered two-dimensional system of independent lattice electrons in a perpendicular magnetic field with rigid confinement in one direction and generalized periodic boundary conditions (GPBC) in the other direction. The…
In electrical metrology, the quantum Hall effect is accessed at the Landau level filling factor {\nu} = 2 plateau to define and disseminate the unit of electrical resistance (ohm). The robustness of the plateau is only exhibited at this…
Hall viscosity, also known as the Lorentz shear modulus, has been proposed as a topological property of a quantum Hall fluid. Using a recent formulation of the composite fermion theory on the torus, we evaluate the Hall viscosities for a…
By numerical exact diagonalization techniques, we obtain the quantum phase diagram of the lattice fractional quantum Hall (FQH) systems in the presence of quenched disorder. By implementing an array of local potential traps representing the…
We briefly review a theoretical picture of the quantum Hall effect in which gauge symmetry of non-relativistic quantum mechanics, the representation theory of U(1)-current algebra, and the study of odd, positive integral quadratic forms on…
A two-dimensional array of quantum dots in a magnetic field is considered. The electrons in the quantum dots are described as unitary random matrix ensembles. The strength of the magnetic field is such that there is half a flux quantum per…
We have conducted an experimental study of the linear transport properties of the magnetic-field induced insulating phase which terminates the quantum Hall (QH) series in two dimensional electron systems. We found that a direct and simple…
A classification of incompressible quantum Hall fluids in terms of integral lattices and arithmetical invariants thereof is proposed. This classification enables us to characterize the plateau values of the Hall conductivity $\sH$ in the…
The recent discovery of the 3D quantum Hall effect in $\mathrm{HfTe_5}$ has also revealed puzzling signatures of possible 3D fractionalization. Beyond the first plateau associated with the lowest Landau band, Hall conductivity exhibits a…
We show that, at low temperatures, macroscopic inhomogeneities of the electron density in the interior of a finite sample cause a reduction in the measured conductivity peak heights $\sigma_{xx}^{\rm max}$ compared to the universal values…
We study finite temperature ($T$) properties of the continuum quantum field theory of systems with a ferromagnetic ground state. A scaling theory of the $T=0$ system is discussed carefully, and its consequences for crossovers between…
We study the quantum phases of spinless fermion at one-third filling on a Kagome lattice featuring a quadratic band touching Fermi point. In the presence of weak first and second nearest-neighbor repulsive interactions ($V_1$ and $V_2$), we…
When phonons couple to fermions in 2D semimetals, the interaction may turn the system into an insulator. There are several insulating phases in which the time reversal and the sublattice symmetries are spontaneously broken. Examples are…
Lattice quantum chromodynamics (QCD) will soon become the primary theoretical tool in rigorous studies of single- and multi-hadron sectors of QCD. It is truly ab initio meaning that its only parameters are those of standard model. The…
It was recently pointed out that topological liquid phases arising in the fractional quantum Hall effect (FQHE) are not required to be rotationally invariant, as most variational wavefunctions proposed to date have been. Instead, they…
The density-density correlation functions (most singular parts) of chiral Luttinger liquids forming the fractional quantum Hall effect (FQHE) edge are systematically derived in presence of a point-contact junction acting as a localised…
We construct a class of lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be controllably solved in their low energy sectors, through a combination of perturbative and…
We present experimental results on the quantized Hall insulator in two dimensions. This insulator, with vanishing conductivities, is characterized by the quantization (within experimental accuracy) of the Hall resistance in units of 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…