  We study the light-cone and front dynamics of a single particle continuous
time extended quantum walk on a one dimensional lattice with finite range
hopping. We show that, in general, for an initially localized state,
propagating wave fronts can be characterized as ordinary or extremal fronts
with the latter exhibiting an anomalous sub-diffusive scaling behaviour in the
front region. We investigate the dynamical global and local scaling properties
of the cumulative probability distribution function for the extended walk with
nearest and next-nearest neighbour hopping using analytical and numerical
methods. The global scaling shows the existence of a 'causal light-cone'
corresponding to excitations travelling with a velocity smaller than a maximal
'light velocity'. Maximal fronts moving with fixed 'light velocity' bound the
causal cone. The front regions spread with time sub-diffusively exhibiting a
local Airy scaling which leads to an internal staircase structure. At a certain
critical next-nearest neighbour hopping strength, there is a transition from a
phase with one 'causal cone' to a phase with two nested 'causal cones' and the
existence of an internal staircase structure in the corresponding cumulative
distribution profiles. We also connect the study to that in spin chain systems
and indicate that a single particle quantum walk on the one dimensional lattice
already captures the many body physics of a spin chain system. In particular,
we suggest that the time evolution of a single particle quantum walk on the one
dimensional lattice with an initially localized state is equivalent to the time
evolution of a domain wall initial state in a corresponding spin chain system.
