Dirac quantum walks on triangular and honeycomb lattices

TL;DR

This paper investigates Dirac quantum walks on triangular and honeycomb lattices, analyzing their properties, differences from the continuous Dirac equation, and effects of electromagnetic coupling, including Bloch oscillations.

Contribution

It introduces a detailed analysis of Dirac quantum walks on non-square lattices and extends them to include electromagnetic interactions.

Findings

Discretized Dirac walks match the continuous Dirac equation in the limit.

Differences in dispersion relations highlight lattice effects.

Electromagnetic coupling induces Bloch oscillations.

Abstract

In this paper, we present a detailed study on discrete-time Dirac quantum walks (DQWs) on triangular and honeycomb lattices. At the continuous limit, these DQWs coincide with the Dirac equation. Their differences in the discrete regime are analyzed through the dispersion relations, with special emphasis on Zitterbewegung. An extension which couples these walks to arbitrary discrete electromagnetic field is also proposed and the resulting Bloch oscillations are discussed.