Fermionic Fractional Chern Insulators Demonstrate Existence of Chiral Graviton Modes

The existence of chiral graviton modes , defining collective excitations found in Fractional Hall liquids , remains a significant challenge for scientists working with solid-state systems. Min Long, Zeno Bacciconi, and Hongyu Lu, alongside colleagues from institutions including The University of Hong Kong, SISSA, and the ICTP, have now presented compelling theoretical and numerical evidence for these modes within fermionic Fractional Chern Insulators. Their research addresses a critical question: can these graviton modes survive on a lattice structure where the symmetries protecting them are diminished? This work is particularly timely given recent progress in creating Fractional Chern Insulators from materials like transition metal dichalcogenides and rhombohedral pentalayer graphene. By establishing a link between these modes in both Fractional Hall and Chern insulator systems, and demonstrating their longevity despite symmetry limitations, the team offers crucial insight for both materials science and cold atom experiments seeking to observe and utilise these exotic excitations.

Researchers employed analytical calculations and numerical simulations to explore the behaviour of these modes in discrete systems, focusing on the interplay between topological protection and lattice symmetry breaking. The primary objective was to determine the conditions under which these modes persist despite the absence of continuous translation and rotation symmetries. The study reveals that chiral graviton modes can indeed survive on the lattice, albeit with a finite lifetime, dependent on the lattice wavevector.

Certain modes exhibit enhanced stability due to quasi-symmetries arising from the discrete structure, and the team identified a novel mechanism for mode localisation at lattice defects, potentially leading to observable signatures in transport experiments. These findings provide crucial insights into the robustness of topological order in condensed matter systems and have implications for the development of quantum devices based on FQH states. Employing a continuum limit expansion, they approximated the system with a continuum fermionic field to simplify analysis and connect lattice behaviour to established FQH theory, defining an effective mass and covariant derivative to understand low-energy excitations. To accurately describe these excitations, scientists developed a lattice stress tensor operator, building upon previous work and guided by the conservation of charge and momentum. This involved meticulously matching the Heisenberg equation for current with the lattice Hamiltonian, carefully cancelling external forces arising from the lattice structure.

The team focused on a scenario with only nearest-neighbor interactions, projecting the Hamiltonian onto a constrained Hilbert space to incorporate interaction effects and calculate the stress tensor components. The research pioneered a method for calculating the diagonal and off-diagonal components of the stress tensor, utilizing discretized current operators and symmetrizing correlated hopping terms to ensure translational invariance. Demonstrating the connection between FQH and FCI states, the team performed an adiabatic interpolation between a low-flux HH model and a Checkerboard lattice model hosting a topological flat band. Experiments revealed an adiabatic connection between FQH and FCI chiral graviton modes through interpolation from a low flux Harper-Hofstadter model to a Checkerboard lattice model hosting a topological flat band. Utilizing state-of-the-art matrix product state and exact diagonalization simulations, the team provided strong evidence that these chiral graviton modes are long-lived excitations in FCIs, even in the absence of continuous symmetries and despite scattering with a two-magnetoroton continuum.

This confirms that geometrical properties and collective excitations of FQH states can survive when transitioning to lattice-based FCIs. A careful finite-size analysis showed that the lattice structure generates a finite, yet small, intrinsic decay rate for the graviton mode. Measurements confirm the existence of a well-defined chiral graviton mode within FCI phases, establishing a clear link to FQH graviton-modes and positioning the graviton as a unifying geometric excitation for both systems. The spectral peak of the graviton mode remains distinguishable despite being embedded within the two-magnetoroton continuum, indicating a robust and measurable excitation. Researchers successfully derived a lattice stress tensor operator, linked to lattice quadrupolar density correlators, within the fermionic Harper-Hofstadter model, demonstrating the existence of graviton modes even without the continuum symmetries typically thought to protect them. The significance of this achievement lies in confirming that these graviton modes are robust, long-lived excitations in fractionalized lattice phases, despite the loss of continuous translational and rotational symmetries.

Analysis revealed a small, intrinsic decay rate for the graviton mode due to lattice effects, indicating that the absence of these symmetries does not immediately eliminate the graviton as a meaningful excitation, but rather introduces a controlled broadening. The identification of short-range quadrupolar density correlators as effective probes of graviton dynamics offers a valuable tool for future experimental investigations. The authors suggest future research could explore these findings in solid-state materials, cavity QED systems, and cold atom experiments, potentially expanding our understanding of geometric collective excitations beyond the traditional Landau level scenario. This work establishes a foundation for exploring graviton modes in realistically constrained systems and provides a pathway for their potential observation in diverse experimental platforms.