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arXiv:2505.02905 · Physical Review Letters

Chiral Graviton Modes on the Lattice

Hernan B. Xavier, Zeno Bacciconi, Titas Chanda, Dam Thanh Son, Marcello Dalmonte

Published Oct 16, 2025• 2 citations
arXivHTMLPDF

Abstract

Chiral graviton modes are elusive excitations arising from the hidden quantum geometry of fractional quantum Hall states. It remains unclear, however, whether this picture extends to lattice models, where continuum translations are broken and additional quasiparticle decay channels arise. We present a framework in which we explicitly derive a field theory incorporating lattice chiral graviton operators within the paradigmatic bosonic Harper-Hofstadter model. Extensive numerical evidence suggests that chiral graviton modes persist away from the continuum and are well captured by the proposed lattice operators. We identify geometric quenches as a viable experimental probe, paving the way for the exploration of chiral graviton modes in near-term quantum simulation experiments.

DOI
10.1103/1636-kl65

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Chiral graviton modes are elusive excitations arising from the hidden quantum geometry of fractional quantum Hall states. It remains unclear, however, whether this picture extends to lattice models, where continuum translations are broken and additional quasiparticle decay channels arise. We present a framework in which we explicitly derive a field theory incorporating lattice chiral graviton operators within the paradigmatic bosonic Harper-Hofstadter model. Extensive numerical evidence suggests that chiral graviton modes persist away from the continuum and are well captured by the proposed lattice operators. We identify geometric quenches as a viable experimental probe, paving the way for the exploration of chiral graviton modes in near-term quantum simulation experiments.
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Intermediate-scale quantum technologies provide unprecedented opportunities for scientific discoveries while posing the challenge of identifying important problems that can take advantage of them through algorithmic innovations. A major open problem in quantum many-body physics is the table-top generation and detection of emergent excitations analogous to gravitons -- the elusive mediators of gravitational force in a quantum theory of gravity. In solid-state materials, fractional quantum Hall phases are one of the leading platforms for realizing graviton-like excitations. However, their direct observation remains an experimental challenge. Here, we generate these excitations on the IBM quantum processor. We first identify an effective one-dimensional model that captures the geometric properties and graviton dynamics of fractional quantum Hall states. We then develop an efficient, optimal-control-based variational quantum algorithm to simulate geometric quench and the subsequent graviton dynamics, which we successfully implement on the IBM quantum computer. Our results open a new avenue for studying the emergence of gravitons in a new class of tractable models that lend themselves to direct implementations on the existing quantum hardware.
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Employing the state-of-the-art time-dependent variational principle (TDVP) algorithm, we compute the spectra of charge-neutral excitations in the ν=1/2ν=1/2ν=1/2 (bosonic) \updated{ and 1/31/31/3 (fermionic) fractional Chern insulator (FCI)} on the Haldane honeycomb lattice model. The magnetoroton visualized from the dynamic density structure factor acquires a minimum gap at finite momentum that can go soft with increasing interaction and give rise to a charge density wave (CDW) at the same wavevector. As the system approaches the FCI-to-CDW transition point, we observe a pronounced sharpening of the roton mode, suggesting that the magnetoroton behaves more like a quasiparticle as it softens. Notably, this occurs while the single-particle gap remains finite. Besides the magnetoroton at finite momentum, we also construct quadrupolar chiral operators in a discrete lattice and resolve the chiral graviton mode around the ΓΓΓ point of the Brillouin zone. Furthermore, we show the different chiralities of the gravitons of FCIs with opposite-sign Hall conductance for the first time.
Intermediate-scale quantum technologies provide new opportunities for scientific discovery, yet they also pose the challenge of identifying suitable problems that can take advantage of such devices in spite of their present-day limitations. In solid-state materials, fractional quantum Hall phases continue to attract attention as hosts of emergent geometrical excitations analogous to gravitons, resulting from the nonperturbative interactions between the electrons. However, the direct observation of such excitations remains a challenge. Here, we identify a quasi-one-dimensional model that captures the geometric properties and graviton dynamics of fractional quantum Hall states. We then simulate geometric quench and the subsequent graviton dynamics on the IBM quantum computer using an optimally compiled Trotter circuit with bespoke error mitigation. Moreover, we develop an efficient, optimal-control-based variational quantum algorithm that can efficiently simulate graviton dynamics in larger systems. Our results open a new avenue for studying the emergence of gravitons in a new class of tractable models on the existing quantum hardware.