Chiral Graviton Theory of Fractional Quantum Hall States

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Du, Yi-Hsien
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866908519177912320
author Du, Yi-Hsien
author_facet Du, Yi-Hsien
contents Recent polarized Raman scattering experiments indicate that fractional quantum Hall systems host a chiral spin-2 neutral collective mode, the long-wavelength limit of the magnetoroton, which behaves as a condensed-matter graviton. We present a nonlinear, gauge-invariant effective theory by gauging area-preserving diffeomorphisms (APDs) with a unimodular spatial metric as the gauge field. A Stueckelberg construction introduces an APD-invariant local potential that aligns the dynamical metric with a reference geometry, opening a tunable gap while preserving gauge redundancy. Together with a geometric Maxwell kinetic sector and the Wen-Zee and gravitational Chern-Simons terms, the theory yields a gapped chiral spin-2 excitation consistent with universal long-wavelength constraints. The tunable gap emerges naturally from symmetry and provides a route to an isotropic-nematic quantum critical point where the spin-2 mode softens. We further establish a linear dictionary to quadrupolar deformations in composite Fermi liquid bosonization, and outline applications to fractional Chern insulators as well as higher-dimensional generalizations. Finally, the approach can be extended to non-Abelian fractional quantum Hall states, capturing both spin-2 and spin-3/2 neutral modes.
format Preprint
id arxiv_https___arxiv_org_abs_2509_04408
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Chiral Graviton Theory of Fractional Quantum Hall States
Du, Yi-Hsien
Strongly Correlated Electrons
Mesoscale and Nanoscale Physics
High Energy Physics - Theory
Recent polarized Raman scattering experiments indicate that fractional quantum Hall systems host a chiral spin-2 neutral collective mode, the long-wavelength limit of the magnetoroton, which behaves as a condensed-matter graviton. We present a nonlinear, gauge-invariant effective theory by gauging area-preserving diffeomorphisms (APDs) with a unimodular spatial metric as the gauge field. A Stueckelberg construction introduces an APD-invariant local potential that aligns the dynamical metric with a reference geometry, opening a tunable gap while preserving gauge redundancy. Together with a geometric Maxwell kinetic sector and the Wen-Zee and gravitational Chern-Simons terms, the theory yields a gapped chiral spin-2 excitation consistent with universal long-wavelength constraints. The tunable gap emerges naturally from symmetry and provides a route to an isotropic-nematic quantum critical point where the spin-2 mode softens. We further establish a linear dictionary to quadrupolar deformations in composite Fermi liquid bosonization, and outline applications to fractional Chern insulators as well as higher-dimensional generalizations. Finally, the approach can be extended to non-Abelian fractional quantum Hall states, capturing both spin-2 and spin-3/2 neutral modes.
title Chiral Graviton Theory of Fractional Quantum Hall States
topic Strongly Correlated Electrons
Mesoscale and Nanoscale Physics
High Energy Physics - Theory
url https://arxiv.org/abs/2509.04408