Twisted quantum walks, generalised Dirac equation and Fermion doubling

Quantum discrete-time walkers have since their introduction demonstrated applications in algorithmics and to model and simulate a wide range of transport phenomena. They have long been considered the discrete-time and discrete space analogue of the Dirac equation and have been used as a primitive to simulate quantum field theories precisely because of some of their internal symmetries. In this paper we introduce a new family of quantum walks, said \textit{twisted}, which admits, as continuous limit, a generalised Dirac operator equipped with a dispersion term. Moreover, this quadratic term in the energy spectrum acts as an effective mass, leading to a regularization of the well known Fermion doubling problem.