Employing the state-of-the-art time-dependent variational principle (TDVP) algorithm, we compute the spectra of charge-neutral excitations in a $\nu =1/2$ (bosonic) 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 wave vector. 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 as 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 $\mathrm{\Gamma }$ point of the Brillouin zone. Furthermore, we show the different chiralities of the gravitons of FCIs with opposite-sign Hall conductance. Our results offer clear spectral observations of the magnetoroton and chiral graviton in FCI lattice models. Our real-space approach paves the way for the tensor-network and quantum Monte Carlo study of the chiral graviton mode.

Close

PrevNext

View figure in article

• Charge density waves
• Chern insulators
• Density matrix renormalization group
• Fractional quantum Hall effect
• Phase transitions
• Honeycomb lattice
• Tensor network methods