Fragile topological phases in interacting systems

TL;DR

This paper extends the concept of fragile topological phases beyond noninteracting electrons, showing they can occur in interacting fermionic and bosonic systems with charge conservation, revealing a broader class of such phases.

Contribution

It demonstrates that fragile topological phases are a general phenomenon present in interacting systems, not limited to noninteracting electrons, under charge conservation symmetry.

Findings

Fragile topology exists in interacting fermionic systems.

Fragile topology also appears in bosonic systems.

Fragile phases are characterized by their susceptibility to trivialization when combined with certain trivial states.

Abstract

Topological phases of matter are defined by their nontrivial patterns of ground-state quantum entanglement, which is irremovable so long as the excitation gap and the protecting symmetries, if any, are maintained. Recent studies on noninteracting electrons in crystals have unveiled a peculiar variety of topological phases, which harbors nontrivial entanglement that can be dissolved simply by the the addition of entanglement-free, but charged, degrees of freedom. Such topological phases have a weaker sense of robustness than their conventional counterparts, and are therefore dubbed "fragile topological phases." In this work, we show that fragile topology is a general concept prevailing beyond systems of noninteracting electrons. Fragile topological phases can generally occur when a system has a $\mathrm{U}(1)$ charge conservation symmetry, such that only particles with one sign of the charge are physically allowed (e.g. electrons but not positrons). We demonstrate that fragile topological phases exist in interacting systems of both fermions and of bosons.