29 research outputs found
Explicit mapping between a 2D quantum Hall system and a 1D Luttinger liquid, I. Luttinger parameters
We study a simple model of a quantum Hall system with the electrons confined
to a linear, narrow channel. The system is mapped to a 1D system which in the
low-energy approximation has the form of a Luttinger liquid with different
interactions between particles of equal and of opposite chiralities. We study
this mapping at the microscopic level, and discuss the relation between the
parameters of the 2D system and the corresponding 1D Luttinger liquid
parameters. We focus in particular on how the parameters are renormalized by
the electron interactions and show that the velocity parameter of the current
is not modified by the interaction.Comment: Latex, 22 pages, 1 figur
Numerical studies of entangled PPT states in composite quantum systems
We report here on the results of numerical searches for PPT states with
specified ranks for density matrices and their partial transpose. The study
includes several bipartite quantum systems of low dimensions. For a series of
ranks extremal PPT states are found. The results are listed in tables and
charted in diagrams. Comparison of the results for systems of different
dimensions reveal several regularities. We discuss lower and upper bounds on
the ranks of extremal PPT states.Comment: 18 pages, 4 figure
Charge Fractionalization on Quantum Hall Edges
We discuss the propagation and fractionalization of localized charges on the
edges of quantum Hall bars of variable widths, where interactions between the
edges give rise to Luttinger liquid behavior with a non-trivial interaction
parameter g. We focus in particular on the separation of an initial charge
pulse into a sharply defined front charge and a broader tail. The front pulse
describes an adiabatically dressed electron which carries a non-integer charge,
which is \sqrt{g} times the electron charge. We discuss how the presence of
this fractional charge can, in principle, be detected through measurements of
the noise in the current created by tunneling of electrons into the system. The
results are illustrated by numerical simulations of a simplified model of the
Hall bar.Comment: 15 page