Ground-state phase diagram of the two-dimensional Bose-Hubbard model with anisotropic hopping

Abstract

We compute the ground state phase diagram of the 2d Bose-Hubbard model with anisotropic hopping using quantum Monte Carlo simulations, connecting the 1d to the 2d system. We find that the tip of the lobe lies on a curve controlled by the 1d limit over the full anisotropy range while the universality class is always the same as in the isotropic 2d system. This behavior can be derived analytically from the lowest RG equations and has a shape typical for the underlying Kosterlitz-Thouless transition in 1d. We also compute the phase boundary of the Mott lobe at unit density for strong anisotropy and compare it to the 1d system. Our calculations shed light on recent cold gas experiments monitoring the dynamics of an expanding cloud.PACS numbers: 03.75. Hh, 64.70.Tg, 05.30.Jp In one dimension, interactions and quantum fluctuations are stronger than in any other dimension. As a consequence, single-particle excitations cannot occur and only collective excitations are formed. The liquids in 1d are known as Luttinger liquids [1], which are critical phases with algebraic correlations. They are for instance susceptible to a lattice when they can form a Mott insulator or to disorder when they can form a Bose glass [2]. A particular kind of relevant perturbations are the ones leading to a dimensional crossover in which Luttinger liquids or 1d systems are coupled with each other in a matrix of higher dimension [3], which can be experimentally realized [4,5]. We will consider hopping processes (that is, a Josephson coupling) between tubes of scalar bosonic Luttinger liquids and Mott insulators arranged in a 2d setup, where the intertube coupling is varied from zero to an equally strong value as the intra-tube coupling. For this 1d-2d crossover, mean-field theory fails [6][7][8], and this topic is one of the remaining open problems in the 1d world [3,9].Recently, studies on dimensional crossovers for fermions have come to the front of attention again. The Mott transition in a frustrated Hubbard model with nextnearest neighbor hopping at half filling on a quasi 1d lattice was studied in Ref.[10], featuring a closing of the 1d Mott gap and supporting the idea that superconductivity is mediated by magnetic fluctuations in organic salts [11]. The situation is reminiscent of the pseudogap phase in high-T c cuprates where enhanced spin fluctuations and spatial correlations in the copper oxide planes occur in the proximity of an insulating phase. The study was extended to dynamical correlation functions in Ref.[12] providing evidence for a dimensional-crossoverdriven confinement of spinons [13]. A 3d Hubbard model with anisotropic hopping was studied with cluster dynamical mean field methods and yielded results in agreement with a cold gas realization for temperatures down to the hopping amplitude [14].In a recent cold gas experiment by Ronzheimer et al.[15] a bosonic system was prepared in the atomic limit in 2d with precisely one particle per site. The experimentalists then quenched the interaction and the hopping along the x and ...

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