PT Journal
AU Arnault, P
   Perez, A
   Arrighi, P
   Farrelly, T
TI Discrete-time quantum walks as fermions of lattice gauge theory
SO Physical Review A
JI Phys. Rev. A
PY 2019
BP 032110
EP 16pp
VL 99
IS 3
DI 10.1103/PhysRevA.99.032110
LA English
AB It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time dynamics is thus not only manifestly unitary, but also ultralocal, i.e., the particle's speed is upper bounded, as in standard relativistic quantum field theories. The lattice chiral symmetry of staggered fermions, which corresponds to a translational invariance, is lost after the requirement of ultralocality of the evolution; this fact is an instance of Meyer's 1996 no-go results stating that no nontrivial scalar quantum cellular automaton can be translationally invariant [D. A. Meyer, J. Stat. Phys. 85, 551 (1996); Phys. Lett. A 223, 337 (1996)]. All results are presented in a single-particle framework and for a (1+1)-dimensional space-time.
ER