Local Commuting Projector Hamiltonians and the Quantum Hall Effect

TL;DR

This paper proves that local commuting projector Hamiltonians cannot exhibit the integer or fractional quantum Hall effects with nonzero Hall conductivity in gapped systems, challenging previous assumptions about their capability to model such phenomena.

Contribution

It establishes a no-go theorem showing the incompatibility of local commuting projector Hamiltonians with nonzero Hall conductivity in gapped quantum Hall systems.

Findings

Local commuting projector Hamiltonians cannot realize quantum Hall effects.

Gapped systems with nonzero Hall conductivity are incompatible with local commuting projector models.

The result constrains theoretical models of topological phases in condensed matter physics.

Abstract

We prove that neither Integer nor Fractional Quantum Hall Effects with nonzero Hall conductivity are possible in gapped systems described by Local Commuting Projector Hamiltonians.