Properties of bosons in a one-dimensional bichromatic optical lattice in the regime of the pinning transition: A worm-algorithm Monte Carlo study

Abstract

The sensitivity of the Sine-Gordon (SG) transition of strongly interacting bosons confined in a shallow, one-dimensional (1D), periodic optical lattice (OL), is examined against perturbations of the OL. The SG transition has been recently realized experimentally by Haller et al. [Nature 466, 597 (2010)] and is the exact opposite of the superfluid (SF) to Mott insulator (MI) transition in a deep OL with weakly interacting bosons. The continuous-space worm algorithm (WA) Monte Carlo method [Boninsegni et al., Phys. Rev. E 74, 036701 (2006)] is applied for the present examination. It is found that the WA is able to reproduce the SG transition which is another manifestation of the power of continuous-space WA methods in capturing the physics of phase transitions. In order to examine the sensitivity of the SG transition, it is tweaked by the addition of the secondary OL. The resulting bichromatic optical lattice (BCOL) is considered with a rational ratio of the constituting wavelengths λ1 and λ2 in contrast to the commonly used irrational ratio. For a weak BCOL, it is chiefly demonstrated that this transition is robust against the introduction of a weaker, secondary OL. The system is explored numerically by scanning its properties in a range of the Lieb-Liniger interaction parameter γ in the regime of the SG transition. It is argued that there should not be much difference in the results between those due to an irrational ratio λ1/λ2 and due to a rational approximation of the latter, bringing this in line with a recent statement by Boéris et al. [Phys. Rev. A 93, 011601(R) (2016)]. The correlation function, Matsubara Green's function (MGF), and the single-particle density matrix do not respond to changes in the depth of the secondary OL V1. For a stronger BCOL, however, a response is observed because of changes in V1. In the regime where the bosons are fermionized, the MGF reveals that hole excitations are favored over particle excitatons manifesting that holes in the SG regime play an important role in the response of properties to changes in γ.