Phase diagram of the two-leg Bose-Hubbard model*

Recently, double-well optical lattices have been created to trap bosonic atoms [J. Sebby-Strabley {\it et al.}, Phys. Rev. A {\bf 73}, 033605 (2006)]. In the present work, we study the superfluid-to-Mott insulator transition of bosons in double-well optical lattices. Applying the time-evolving block decimation algorithm [G. Vidal, Phys. Rev. Lett. {\bf 93}, 040502 (2004); cond-mat/0605597] to the two-leg Bose-Hubbard Hamiltonian, we obtain the zero-temperature phase diagrams and find that there are the half-integer-filling and integer-filling Mott insulator regions. For symmetric double wells (no tilt), we show that the half-integer-filling Mott insulator phase is stabilized and that the integer-filling Mott insulator domain becomes smaller as the intra-double-well hopping increases. As the tilt of the double-wells increases, we find that the half-integer-filling Mott insulator phase becomes larger monotonically and approaches the integer-filling Mott phase for a single 1D lattice. In contrast, we show that the integer-filling Mott phase shows non-monotonic reentrant behaviour as a function of the tilt parameter.