  Since the discovery of half-filled cuprate to be a Mott insulator, the
excitation spectra above the chemical potential for the unoccupied states has
attracted many research attentions. There were many theoretical works using
different numerical techniques to study this problem, but many have reached
different conclusions. One of the reasons is the lack of very detailed
high-resolution experimental results for the theories to be compared with.
Recently, the scanning tunneling spectroscopy
(STS)\cite{cai2015visualizing,ye2013visualizing} on lightly doped Mott
insulator with an antiferromagnetic (AFM) order found the presence of in-gap
states with energy of order half an eV above the chemical potential. The
measured spectral properties with doping are not quite consistent with earlier
theoretical works. In this paper we perform a diagonalization method on top of
the variational Monte Carlo (VMC) calculation to study the evolution of AFM
Mott state with doped hole concentration in the Hubbard model (HM). Our results
found in-gap states that behave similarly with ones reported by STS. These
in-gap states acquire a substantial amount of dynamical spectral weight
transferred from the upper Hubbard band. The in-gap states move toward chemical
potential with increasing spectral weight as doping increases. Our result also
provides information about the energy scale of these in-gap states in relation
with the coulomb coupling strength U.
