Landau levels for discrete-time quantum walks in artificial magnetic fields

TL;DR

This paper introduces a new family of 2D discrete-time quantum walks that replicate Dirac fermion dynamics in magnetic fields, constructing Landau levels both in the continuous limit and for finite steps, supported by numerical simulations.

Contribution

It presents a novel family of quantum walks that accurately model magnetic field effects and Landau levels, extending their validity beyond the continuous limit.

Findings

Landau levels constructed for finite steps via perturbative approach

Numerical simulations confirm the magnetic interpretation beyond the continuous limit

Quantum simulation potential for condensed-matter systems discussed

Abstract

A new family of 2D discrete-time quantum walks (DTQWs) is presented and shown to coincide, in the continuous limit, with the Dirac dynamics of a spin 1/2 fermion coupled to a constant and uniform magnetic field. Landau levels are constructed, not only in the continuous limit, but also for the DTQWs i.e. for finite non-vanishing values of the time- and position-step, by a perturbative approach in the step. Numerical simulations support the above results and suggest that the magnetic interpretation is valid beyond the scope of the continuous limit. The possibility of quantum simulation of condensed-matter systems by DTQWs is also discussed.