Phases of the one-dimensional Bose-Hubbard model

Abstract

The zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with nearestneighbor interaction is investigated using the Density-Matrix Renormalization Group. Recently normal phases without long-range order have been conjectured between the charge density wave phase and the superfluid phase in one-dimensional bosonic systems without disorder. Our calculations demonstrate that there is no intermediate phase in the one-dimensional Bose-Hubbard model but a simultaneous vanishing of crystalline order and appearance of superfluid order. The complete phase diagrams with and without nearest-neighbor interaction are obtained. Both phase diagrams show reentrance from the superfluid phase to the insulator phase.PACS numbers: 05.30. Jp, 05.70.Jk, 67.40.Db Quantum phase transitions in strongly correlated systems have attracted a lot of interest in recent years. Usually the basic particles are electrons, but in some interesting cases the relevant particles are not fermions but bosons. Examples of experimental systems with superfluid and insulating phases are Cooper pairs in thin granular superconducting films 1 and cooper pairs or fluxes in Josephson junction arrays 2 . While in dimensions greater than one the existence of supersolids 3 , i.e. phases with simultaneous superfluid and crystalline order, has been established in theoretical work, the situation in one dimension is less clear. Recently normal phases that are neither crystalline nor superfluid have been found in a one-dimensional model of Josephson junction arrays 4 in the region where supersolids are found in higher dimensions. In this paper we will verify whether supersolids or normal phases exist in the more general Bose-Hubbard model in one dimension.The Bose-Hubbard model contains the basic physics of interacting bosons on a lattice. It is a minimal bosonic many-particle model that cannot be reduced to a single particle model. The bosons have repulsive interactions, and they can gain energy by hopping to neighboring sites on the lattice. The Hamiltonian with on-site and nearestneighbor interactions iswhere b i are the annihilation operators of bosons on site i,n i = b † i b i the number of particles on site i, t is the hopping matrix element. U and V are on-site and nearestneighbor repulsion, and µ is the chemical potential. The energy scale is set by choosing U = 1.The range of the interactions depends on the individual experimental situation. In general the lattice underlying the system is not an atomic lattice, but a larger structure like a Josephson-junction or a grain in a superconductor. In Josephson-junctions the relevant bosons can be cooper pairs or fluxes, resulting in different interactions.As a starting point we first consider the case of onsite repulsion only. In the (µ, t)-plane Mott-insulating regions are surrounded by the superfluid phase 5 . These phases are separated by two types of phase transitions. On the constant density line the transition is driven by phase fluctuations and is of the Berezinskii-KosterlitzThouless (BKT...

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