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Bose—Hubbard Model in Checkerboard Superlattices with a Magnetic Field

In this paper we investigate classical and quantum phase transitions of Bose—Hubbard model in checkerboard superlattices with a magnetic field at the mean-field level. By analyzing stability of normal state phase boundaries are obtained analytically for zero and finite temperature in a unified theoretical frame and easily extended to the situation without the magnetic field. All results illustrate that the introduction of the magnetic field enhances the stability of normal state and Mott insulator. In addition we also note that the critical hopping term presents an oscillating behavior inversely following the upper boundary of Hofstadter butterfly.