  The energy of one hole in one dimensional Ising antiferromagnet is calculated
using exact diagonalization (ED) method on finite systems with number of sites
N ranging from 4 to 50. This study gives a power-law description for the hole
energy in the weak coupling region (0.001 less than or equal to Jz/t and Jz/t
less than or equal to 0.1).This power-law description can otherwise be
understood as a weak string-like energy that tends to compromise the motion of
the hole by confining it to its birth site. However, for large N, the hole is
found to escape from this confinement and hence propagates as a free particle
in agreement with theoretical results in the bulk limit and experimental
observations from angle resolved photoemission spectroscopy (ARPES) of
spin-charge separation. In the strong coupling regime (Jz/t greater than 1),
the energy of the hole is found to be independent of the system size.
Accordingly, the velocities corresponding to charge and spin degrees of freedom
in this regime become comparable. Under this situation, the hole may be treated
as a localized particle.
