On the magneto-roton gap and the Laughlin state stability

TL;DR

This paper critically examines the GMP evaluation of the magneto-roton spectrum, arguing it does not confirm the Laughlin state's variational stability and estimating corrections that suggest lower energy states exist.

Contribution

It provides an analysis showing that the GMP spectrum does not guarantee Laughlin state stability and estimates necessary corrections for a variational approach.

Findings

GMP spectrum does not imply Laughlin state stability

Lower energy states exist at certain wavevectors

Corrections suggest possible variational instability

Abstract

It is argued that the Girvin, MacDonald and Platzman (GMP) evaluation of the magneto-roton spectrum, in spite of probably being a sensible estimate of the excitation spectrum around the real ground state, is not implying the variational stability of the Laughlin state. The suplementary corrections needed to produce a variational calculation around the Laughlin state at 1/3 value of the filling factor are evaluated approximately. The results indicate, within the considered approximation, the existence of lower lying states for a range of wavevector values.