Topological characterization of periodically-driven quantum systems

TL;DR

This paper explores the topological classification of periodically driven quantum systems using Floquet operators, revealing new phases and explaining phenomena like quantized adiabatic pumping with intuitive spectral interpretations.

Contribution

It introduces a topological classification scheme for Floquet operators in driven systems and demonstrates novel phases, including edge modes in topologically trivial bulk systems.

Findings

Floquet operators can be divided into topologically distinct classes.

The classification provides an intuitive spectral interpretation.

A driven hexagonal lattice model exhibits multiple topological phases.

Abstract

Topological properties of physical systems can lead to robust behaviors that are insensitive to microscopic details. Such topologically robust phenomena are not limited to static systems but can also appear in driven quantum systems. In this paper, we show that the Floquet operators of periodically driven systems can be divided into topologically distinct (homotopy) classes, and give a simple physical interpretation of this classification in terms of the spectra of Floquet operators. Using this picture, we provide an intuitive understanding of the well-known phenomenon of quantized adiabatic pumping. Systems whose Floquet operators belong to the trivial class simulate the dynamics generated by time-independent Hamiltonians, which can be topologically classified according to the schemes developed for static systems. We demonstrate these principles through an example of a periodically driven two--dimensional hexagonal lattice model which exhibits several topological phases. Remarkably, one of these phases supports chiral edge modes even though the bulk is topologically trivial.