Quantum Hall Dynamics on Von Neumann Lattice

Flux State in Von Neumann Lattice and Fractional Hall Effect

Formulation of quantum Hall dynamics using von Neumann lattice of guiding center coordinates is presented. A topological invariant expression of the Hall conductance is given and a new mean field theory of the fractional Hall effect based on flux condensation is proposed. Because our mean field Hamiltonian has the same form as Hofstadter Hamiltonian, it is possible to understand characteristic ...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Is Hall Conductance in Hall Bar Geometry a Topological Invariant ?

A deep connection between the Hall conductance in realistic situation and a topological invariant is pointed out based on von-Neumann lattice representation in which Landau level electrons have minimum spatial extensions. We show that the Hall conductance has no finite size correction in quantum Hall regime, but a coefficient of induced Chern-Simons term in QED 3 has a small finite size correct...

Anisotropy in the Compressible Quantum Hall State

Using a mean field theory on the von Neumann lattice, we study compressible anisotropic states around ν = l+ 1/2 in the quantum Hall system. The Hartree-Fock energy of the UCDW are calculated self-consistently. In these states the unidirectional charge density wave (UCDW) seems to be the most plausible state. We show that the UCDW is regarded as a collection of the one-dimensional lattice fermi...

Entanglement entropy and multifractality at localization transitions

The von Neumann entanglement entropy is a useful measure to characterize a quantum phase transition. We investigate the nonanalyticity of this entropy at disorder-dominated quantum phase transitions in noninteracting electronic systems. At these critical points, the von Neumann entropy is determined by the single particle wave function intensity, which exhibits complex scale invariant fluctuati...