Chiral Graviton Theory of Fractional Quantum Hall States
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908519177912320 |
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| 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 |