Topologically Protected Edge Modes in Gapless Floquet Systems with Chiral Symmetry

Core Concepts

This paper reveals that periodically driven systems with chiral symmetry can exhibit robust topological edge modes even without bulk energy gaps, extending the traditional understanding of topological phases and bulk-boundary correspondence.

Abstract

• Bibliographic Information: Cardoso, G., Yeh, H., Korneev, L., Abanov, A. G., & Mitra, A. (2024). Gapless Floquet topology. arXiv:2411.02526v1 [cond-mat.str-el].

• Research Objective: This research paper investigates the existence and robustness of topological edge modes in periodically driven (Floquet) systems with chiral symmetry, specifically focusing on scenarios where the bulk energy spectrum lacks gaps.

• Methodology: The authors employ theoretical analysis based on the half-period decomposition of chiral evolutions to construct topological invariants that circumvent the need for a defined Floquet Hamiltonian. They provide explicit examples, including generalizations of the Kitaev chain and related spin models, to demonstrate their findings. Numerical simulations are also used to study the effect of interactions on edge mode stability.

• Key Findings: The study reveals that topological edge zero- and π-modes can persist even in the absence of bulk gaps in the quasienergy spectrum of Floquet systems with chiral symmetry. The authors introduce new topological invariants that remain well-defined in the gapless regime and establish a generalized bulk-boundary correspondence principle relating these invariants to the number of edge modes. They demonstrate that interactions can induce a finite lifetime for edge modes, with the decay rate scaling polynomially with interaction strength.

• Main Conclusions: The research significantly extends the concept of topological phases and bulk-boundary correspondence to gapless Floquet systems. It provides a theoretical framework for understanding and predicting the existence of robust edge modes in these systems, even when traditional topological invariants based on bulk gaps are not applicable.

• Significance: This work has significant implications for the study of topological phases in driven systems, particularly in contexts where gaplessness is inherent or induced by external factors. It opens new avenues for exploring exotic topological phenomena and potential applications in areas like quantum information processing and topological photonics.

• Limitations and Future Research: The study primarily focuses on one-dimensional systems. Extending the analysis to higher dimensions and exploring the interplay of gapless Floquet topology with other symmetries and topological classifications are promising directions for future research. Further investigation into the dynamics and potential applications of these robust edge modes in gapless Floquet systems is also warranted.

Stats

Quotes

Key Insights Distilled From

Gapless Floquet topology

by Gabriel Card... at arxiv.org 11-06-2024

https://arxiv.org/pdf/2411.02526.pdf