Density Matrix Renormalization Group Study of a Lowest Landau Level Electron Gas on a Thin Cylinder

TL;DR

This study uses the Density Matrix Renormalization Group to analyze the ground state of a 2D electron gas in the lowest Landau level on a thin cylinder, revealing a charge density wave state generally, but a homogeneous gapless state at filling factor 1/2.

Contribution

It applies DMRG to a cylindrical geometry to explore ground states of the lowest Landau level, highlighting a unique gapless state at ν=1/2.

Findings

Charge density wave state at generic filling factors

Homogeneous gapless state at ν=1/2

Study of particle and hole excitations at ν=1/2

Abstract

We investigate the ground state properties of a two-dimensional electron gas in the lowest Landau level using the Density Matrix Renormalization Group. The electron gas is confined to a cylinder with a strong magnetic field perpendicular to the surface. For a thin cylinder, the ground state is for generic filling factors a charge density wave state, however, at $\nu=1/2$ a homogeneous and apparently gapless ground state is found and particle and hole excitations are studied.