We report a systematic study of the transition from a band insulator (BI) to
a Mott insulator (MI) in a one-dimensional Hubbard model at half-filling with
an on-site Coulomb interaction U and an alternating periodic site potential V.
We employ both the zero-temperature density matrix renormalization group (DMRG)
method to determine the gap and critical behavior of the system and the
finite-temperature transfer matrix renormalization group method to evaluate the
thermodynamic properties. We find two critical points at U = Uc and U =
Us that separate the BI and MI phases for a given V. A charge-neutral
spin-singlet exciton band develops in the BI phase (U<Uc) and drops below
the band gap when U exceeds a special point Ue. The exciton gap closes at the
first critical point Uc while the charge and spin gaps persist and coincide
between Uc<U<Us where the system is dimerized. Both the charge and spin
gaps collapse at U = Us when the transition to the MI phase occurs. In the
MI phase (U>Us) the charge gap increases almost linearly with U while the
spin gap remains zero. These findings clarify earlier published results on the
same model, and offer insights into several important issues regarding an
appropriate scaling analysis of DMRG data and a full physical picture of the
delicate nature of the phase transitions driven by electron correlation. The
present work provides a comprehensive understanding for the critical behavior
and phase diagram for the transition from BI to MI in one-dimensional
correlated electron systems with a periodic alternating site potential.Comment: long version, 10 figure