Gapless Flat Bands Enable Fractional Quantization with Divergent Quantum Geometry

The pursuit of the fractional anomalous Hall (FQAH) effect, a promising route towards robust quantum computing and a deeper understanding of electron interactions, typically relies on the properties of ideal flat bands within materials. Wenqi Yang, Dawei Zhai, and Wang Yao, all from The University of Hong Kong, now demonstrate that FQAH states can also emerge in a surprisingly different setting, materials featuring gapless flat bands with unusual geometric properties. Their calculations reveal a robust FQAH phase that persists regardless of the strength of electron interactions, a significant departure from existing understanding. This achievement expands the possibilities for designing materials exhibiting the FQAH effect and opens new avenues for exploring the complex interplay between geometry and electron behaviour in flat-band systems.

Lattice Models, Convergence, and Computational Details

This document provides supporting information for research on fractional quantum Hall physics in Kagome and Honeycomb lattices, explaining the single-particle lattice models used and validating results through rigorous testing. The research focuses on understanding the behaviour of electrons in these materials and confirming the existence of exotic quantum states. Scientists performed extensive calculations to confirm the stability of observed phases and ensure the reliability of their findings. Key findings reveal the existence of fractional quantum Hall (FQAH) phases in both the Honeycomb and Kagome lattices, characterized by Laughlin-like behaviour observed in entanglement and energy spectra. Calculations demonstrate the existence of topological gaps, indicating the robustness of these phases, and explore how these phases depend on parameters such as interaction strength and model characteristics.

Singular Flat Bands and Fractional Anomalous Hall Effect

Scientists investigated the fractional anomalous Hall (FQAH) effect by exploring unconventional flat band scenarios beyond traditional models, focusing on singular flat bands with unique geometric properties. Researchers constructed models based on honeycomb and kagome geometries, allowing them to tune the quantum geometry and investigate its impact on FQAH states. Through exact diagonalization and density matrix renormalization group calculations, the team mapped out the many-body phase diagrams for both models, discovering that FQAH phases persist even with strong interactions and varying degrees of geometric distortion. Further analysis revealed that the stability of these phases depends on the system’s ability to adapt to complex landscapes by developing an inhomogeneous carrier distribution, repelling interacting carriers to maintain the FQAH phase even near points of high geometric divergence.

Gapless Flat Bands Enable Robust Fractional Hall Effect

Scientists have discovered a robust fractional anomalous Hall (FQAH) effect in materials featuring gapless flat bands, challenging previous understanding of this quantum phenomenon. Through exact diagonalization and density matrix renormalization group calculations, the team demonstrated the persistence of FQAH phases across a broad range of interaction strengths. Measurements reveal that the stability of these FQAH states doesn’t directly correlate with the strength of geometric fluctuations. Instead, the many-body order adapts to the complex geometric landscape by spontaneously developing an inhomogeneous carrier distribution.

This adaptability is confirmed by observing that the quenching of the FQAH phase coincides with a decrease in the occupation-weighted Berry flux, a measure of the geometric properties of the electronic bands. The team constructed honeycomb and kagome models to explore these effects, demonstrating that FQAH phases are maintained even with tunable quantum geometry divergence. Remarkably, calculations demonstrate a fractionally quantized Hall conductivity, confirming the FQAH phase. The momentum-resolved entanglement spectrum exhibits characteristics of Laughlin states, providing further evidence for topological order. These findings demonstrate a profound interplay between geometry and many-body correlations, significantly expanding the design space for exploring FQAH effects and flat-band correlation phenomena.

Gapless Flat Bands Support Fractional Hall States

This research demonstrates the emergence of fractional anomalous Hall (FQAH) phases in materials possessing gapless flat bands, challenging the conventional understanding that such phases require ideal flat Chern bands. Through detailed calculations, scientists established that FQAH states can persist independently of interaction strength, remaining stable even in strongly correlated systems. This finding broadens the scope for designing materials that exhibit this intriguing quantum phenomenon. Measurements reveal that the stability of these FQAH states doesn’t depend solely on the strength of geometric singularities or fluctuations.

Instead, the system adapts to these complex geometric landscapes by spontaneously creating an uneven distribution of charge carriers, maintaining the FQAH phase as long as a certain level of occupation-weighted Berry flux is maintained. Investigations using a kagome lattice model revealed that while strong electron localization can lead to a transition to a charge density wave phase, the FQAH phase can be sustained across a range of parameters. This research significantly expands the possibilities for exploring FQAH effects and flat-band correlations, offering new avenues for materials discovery and quantum technologies.