Boundary Conditions for Bulk and Edge States in Quantum Hall Systems

TL;DR

This paper develops boundary conditions for 2D Schrödinger Hamiltonians that distinguish between bulk and edge states, providing insights into quantum Hall systems and their edge-bulk state separation.

Contribution

It introduces a method to split the Hilbert space into chiral boundary states and bulk states, specifically applied to quantum Hall systems with magnetic fields.

Findings

Boundary conditions effectively separate edge and bulk states.

Application to integer and fractional quantum Hall effects.

Discussion of open problems in quantum Hall physics.

Abstract

For two dimensional Schroedinger Hamiltonians we formulate boundary conditions that split the Hilbert space according to the chirality of the eigenstates on the boundary. With magnetic fields, and in particular, for Quantum Hall Systems, this splitting corresponds to edge and bulk states. Applications to the integer and fractional Hall effect and some open problems are described.