Fractional quantization by interaction of arbitrary strength in gapless flat bands with divergent quantum geometry

TL;DR

This paper demonstrates the emergence of fractional quantum anomalous Hall states in gapless flat bands with divergent quantum geometry, challenging the conventional paradigm of ideal flat Chern bands.

Contribution

It uncovers the stability of FQAH phases in non-ideal, gapless flat bands with divergent quantum geometry, expanding the understanding of topological states beyond traditional flat Chern bands.

Findings

FQAH states persist across all interaction strengths in gapless flat bands.

FQAH stability is not solely determined by quantum geometric fluctuations.

Many-body topological order adapts to quantum geometric landscape via inhomogeneous carrier distribution.

Abstract

Fractional quantum anomalous Hall (FQAH) effect, a lattice analogue of fractional quantum Hall effect, offers a unique pathway toward fault-tolerant quantum computation and deep insights into the interplay of topology and strong correlations. The exploration has been successfully guided by the paradigm of ideal flat Chern bands, which mimic Landau levels in both band topology and local quantum geometry. Yet, given the boundless potential for Bloch bands in lattice systems, it remains a significant open question whether FQAH states can arise in scenarios fundamentally distinct from this paradigm. Here we turn to a class of gapless flat bands, featuring (i) ill-defined band topology, (ii) non-quantized Berry flux, (iii) divergent quantum geometry at singular band touchings, (iv) highly fluctuating and far-from-ideal quantum geometry across the Brillouin zone (BZ). Our exact diagonalization and density matrix renormalization group calculations unambiguously demonstrate FQAH phase that is virtually independent of the interaction strength, persisting from the weak-interaction to the strong-interaction limit. We find the stability of the FQAH states does not uniquely correlate with the singularity strength or the BZ-averaged quantum geometric fluctuations. Instead, the many-body topological order can adapt to the singular and fluctuating quantum geometric landscape by spontaneously developing an inhomogeneous carrier distribution, while its quenching accompanies the drop in the occupation-weighted Berry flux. Our work reveals a profound interplay between local quantum geometry and many-body correlation, and significantly expands the exploration space for FQAH effect and correlated phenomena in general.