Six-dimensional time-space crystalline structures

TL;DR

This paper introduces the concept of six-dimensional time-space crystalline structures, demonstrating their potential to realize complex quantum phenomena like the six-dimensional quantum Hall effect through combined temporal and spatial regularity.

Contribution

It presents a novel theoretical framework for six-dimensional time-space lattices and shows their ability to exhibit higher-dimensional quantum Hall effects.

Findings

Six-dimensional time-space lattices can be theoretically constructed.

Such structures can realize the six-dimensional quantum Hall effect.

The third Chern number quantifies the effect in these lattices.

Abstract

Time crystalline structures are characterized by regularity that single-particle or many-body systems manifest in the time domain, closely resembling the spatial regularity of ordinary space crystals. Here we show that time and space crystalline structures can be combined together and even six-dimensional time-space lattices can be realized. As an example, we demonstrate that such time-space crystalline structures can reveal the six-dimensional quantum Hall effect quantified by the third Chern number.