Resolving Geometric Excitations of Fractional Quantum Hall States

TL;DR

This paper uses tensor-network methods to analyze the neutral excitations in fractional quantum Hall states, revealing complex spectra and supporting the existence of emergent supersymmetry, advancing understanding of long-wavelength excitations.

Contribution

It introduces a novel tensor-network approach to study long-wavelength neutral excitations in fractional quantum Hall states, uncovering complex spectra and emergent supersymmetry.

Findings

Identification of $S=-2$ geometric excitations.

Unveiling complex spectra of neutral fermion and bosonic modes.

Support for emergent supersymmetry hypothesis.

Abstract

The quantum dynamics of the intrinsic metric profoundly influence the neutral excitations in the fractional quantum Hall system, as established by Haldane in 2011 \cite{Haldane2011}, and further evidenced by a recent two-photon experiment \cite{Liang2024}. Despite these advancements, a comprehensive understanding of the dynamic properties of these excitations, especially at long wavelengths, continues to elude interest. In this study, we employ tensor-network methods to investigate the neutral excitations of the Laughlin and Moore-Read states on an infinite cylinder. This investigation deepens our understanding of the excitation spectrum in regions where traditional methods do not work effectively. The spectral functions for both states reveal the presence of $S=-2$ geometric excitations. For the first time, we unveil the complex spectra of both neutral fermion and bosonic Girvin-MacDonald-Platzman modes within the excitation continuum by calculating the three-particle density response function for the Moore-Read state. Our findings support the hypothesis of emergent supersymmetry and highlight the potential for detecting neutral fermions in future experiments.