https://doi.org/10.1140/epjd/s10053-023-00659-9
Regular Article – Quantum Information
Twisted quantum walks, generalised Dirac equation and Fermion doubling
1
Ecole Normale Supérieure de Lyon, Lyon, France
2
MINES Paris, Université PSL, Paris, France
3
CNRS, LIS, Aix-Marseille Université, Université de Toulon, Marseille, France
b
giuseppe.dimolfetta@lis-lab.fr
Received:
30
December
2022
Accepted:
24
April
2023
Published online:
24
May
2023
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 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.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
