Does a Fractional Quantum Hall Edge Have a Protected Intrinsic Dipole Moment?

TL;DR

This study critically examines claims of a protected intrinsic dipole moment at fractional quantum Hall edges, revealing it only in specific cases and challenging previous assumptions.

Contribution

The paper employs DMRG methods to accurately compute edge dipoles, showing that the intrinsic dipole is only present at certain filling factors, contrary to prior claims.

Findings

Intrinsic dipole only at ν=1/3 edge

Other edges do not exhibit protected intrinsic dipoles

Hierarchy states likely lack protected intrinsic dipoles

Abstract

We investigate the claims by Park and Haldane [Phys. Rev. B 90, 045123 (2014)] of an intrinsic protected value of the electric dipole moment at the physical edge of fractional quantum Hall (FQH) systems. Contrary to prevailing expectations, we find that the edge dipole takes the expected intrinsic value only in certain very special cases. We identify key limitations in earlier numerical studies and employ density matrix renormalization group (DMRG) methods to accurately compute the ground-state dipole. We focus on three representative systems: the $\nu=1/3$-vacuum edge, the $\nu=2/3$-vacuum edge, and the interface between Pfaffian and anti-Pfaffian phases. We find that the expected intrinsic dipole value occurs only at $\nu=1/3$, whereas the other systems do not exhibit the claimed intrinsic value. We give arguments based on composite fermions as to why hierarchy states should generally not have protected intrinsic dipoles. These results have important implications for the energetics and edge structure of FQH states.