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 pinning transition (PT) as described by the sine-Gordon model of strongly interacting bosons confined in a shallow, one-dimensional, periodic optical lattice (OL), is examined against perturbations of the OL. The PT has been recently realized experimentally by Haller et al. [Nature (London) 466, 597 (2010)] and is the exact opposite of the superfluid-to-Mott-insulator 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 PT, 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 PT, 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 ${\ensuremath{\lambda}}_{1}$ and ${\ensuremath{\lambda}}_{2}$ in contrast to the commonly used irrational ratio. For a weak BCOL, it is chiefly demonstrated that this PT 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 $\ensuremath{\gamma}$ in the regime of the PT. It is argued that there should not be much difference in the results between those due to an irrational ratio ${\ensuremath{\lambda}}_{1}/{\ensuremath{\lambda}}_{2}$ and those due to a rational approximation of the latter, bringing this in line with a recent statement by Boers et al. [Phys. Rev. A 75, 063404 (2007)]. 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 ${V}_{1}$. For a stronger BCOL, however, a response is observed because of changes in ${V}_{1}$. In the regime where the bosons are fermionized, the MGF reveals that hole excitations are favored over particle excitations manifesting that holes in the PT regime play an important role in the response of properties to changes in $\ensuremath{\gamma}$.