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We report a systematic study of the transition from a band insulator (BI) toa Mott insulator (MI) in a one-dimensional Hubbard model at half-filling withan 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 thefinite-temperature transfer matrix renormalization group method to evaluate thethermodynamic properties. We find two critical points at U = $U_c$ and U =$U_s$ that separate the BI and MI phases for a given V. A charge-neutralspin-singlet exciton band develops in the BI phase (U<$U_c$) and drops belowthe band gap when U exceeds a special point Ue. The exciton gap closes at thefirst critical point $U_c$ while the charge and spin gaps persist and coincidebetween $U_c$<U<$U_s$ where the system is dimerized. Both the charge and spingaps collapse at U = $U_s$ when the transition to the MI phase occurs. In theMI phase (U>$U_s$) the charge gap increases almost linearly with U while thespin gap remains zero. These findings clarify earlier published results on thesame model, and offer insights into several important issues regarding anappropriate scaling analysis of DMRG data and a full physical picture of thedelicate nature of the phase transitions driven by electron correlation. Thepresent work provides a comprehensive understanding for the critical behaviorand phase diagram for the transition from BI to MI in one-dimensionalcorrelated electron systems with a periodic alternating site potential.Comment: long version, 10 figure

Transition from band insulator to Mott insulator in one dimension: Critical behavior and phase diagram