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

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. •Explicit construction of discrete-time quantum walks (DTQWs) whose continuous limit coincides with the dynamics of a Dirac fermion coupled to a magnetic field.•Construction of Landau levels for these DTQWs.•Results show that DTQWs can be used as quantum simulators of magnetic effects in condensed matter.