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arXiv · 2501.00247

Spectra of Magnetoroton and Chiral Graviton Modes of Fractional Chern Insulator

Min Long·Hongyu Lu·Han-Qing Wu·Zi Yang Meng
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Abstract

Employing the state-of-the-art time-dependent variational principle (TDVP) algorithm, we compute the spectra of charge-neutral excitations in the $\nu=1/2$ (bosonic) \updated{ and $1/3$ (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 $\Gamma$ 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.

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Min Long, Hongyu Lu, Han-Qing Wu, Zi Yang Meng. 2024-12-31. Spectra of Magnetoroton and Chiral Graviton Modes of Fractional Chern Insulator. https://doi.org/10.1103/bjrf-b8s9

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