A numerical exact solution of the Bose-Hubbard model
Physikalisches Institut, Universit¨at Bonn, Nusallee 12, D-53115 Bonn, Germany(February 1, 2008)In this paper we report results from a systematic strong-coupling expansion of the Bose-Hubbardmodel in one and two spatial dimensions. We obtain numerically exact results for the structurefactor and the spectrum of single particle and single hole excitations in the Mott insulator. Thisenables the determination of the zero-temperature phase diagram and the location of the criticalendpoints of the Mott lobes. In one dimension we conﬁrm the occurrence of reentrance behaviorfrom the compressible to the insulating phase in a region close to the critical point.PACS numbers: 05.30.Jp, 05.70.Jk, 67.40.DbI. INTRODUCTION