  We introduce the Peierls substitution to a two-dimensional discrete-time
quantum walk on a square lattice to examine the spreading dynamics and the
coin-position entanglement in the presence of an artificial gauge field. We use
the ratio of the magnetic flux through the unit cell to the flux quantum as a
control parameter. For a given flux ratio, we obtain faster spreading for a
small number of steps and the walker tends to be highly localized around the
origin. Moreover, the spreading of the walk can be suppressed and decreased
within a limited time interval for specific rational values of flux ratio. When
the flux ratio is an irrational number, even for a large number of steps, the
spreading exhibit diffusive behavior rather than the well-known ballistic one
as in the classical random walk and there is a significant probability of
finding the walker at the origin. We also analyze the coin-position
entanglement and show that the asymptotic behavior vanishes when the flux ratio
is different from zero and the coin-position entanglement become nearly maximal
in a periodic manner in a long time range.
