Numerical study of the FQHE edge Luttinger liquid

Nikolay V. Prokof'ev

Shivakumar Jolad, Chia‐Chen Chang, Jainendra Jain

Wenjun Zheng

We derive a microscopic theory of the composite particles describing the low-lying edge excitations in the fractional quantum Hall liquid with ν=1/m. Using the composite-particle transformation, one finds that the edge states of the system in a disc sample are described by the Calogero–Sutherland model with other interactions between the composite particles as perturbations. The effects of both the interactions and the confinement potential are considered, and proved unable to change the exponent g=ν=1/m. We also obtain the important chiral condition at the mean field level, and as a result justify microscopically the Chiral Luttinger Liquid model of the FQHE edge states.

Adrian Del Maestro

Fedor Vasilievich Kusmartsev, Alan H. Luther, A. A. Nersesyan

J. Silva-Valencia, E. Miranda, Raimundo R. dos Santos

We calculate the correlation functions and the dc conductivity of Luttinger liquid superlattices, modelled by a repeated pattern of interacting and free Luttinger liquids. In a specific realization, where the interacting subsystem is a Hubbard chain, the system exhibits a rich phase diagram with four different phases: two metals and two compressible insulators. In general, we find that the effective low-energy description amalgamates features of both types of liquids in proportion to their spatial extent, suggesting the interesting possibility of `engineered' Luttinger liquids. In recent years, new experimental techniques have made it possible to grow nanostructures which are topologically one-dimensional, such as quantum wires and Carbon nanotubes. However, care must be taken when invoking existing models to discuss their electronic properties, since inhomogeneities must be taken into account in a fundamental way. Consider, for instance, the Luttinger liquid (LL), which is the standard model for low-energy phenomena involving interacting electrons in one dimension [1]. The absence of conductance renormalization in long high-mobility GaAs wires [2] has been explained in terms of a usual LL (representing the wire) in contact with a non-interacting LL at each of its ends (representing the Fermi liquid leads); that is, overall, the system can be thought of as an inhomogeneous Luttinger Liquid (ILL). LLs with different inhomogeneity profiles have also been used in the context of the fractional quantum Hall effect (FQHE), to describe transitions between edge states at different fillings [3, 4], or between an edge state connected to a Fermi liquid [5]. A different class of inhomogeneous systems is represented by superlattices (SLs) and multilayers. By varying the relative th...