Properties of bosons in a one-dimensional bichromatic optical lattice in the regime of the Sine-Gordon transition: a Worm Algorithm Monte Carlo study

TL;DR

This study uses Worm Algorithm Monte Carlo simulations to explore how interacting bosons behave in a one-dimensional bichromatic optical lattice, focusing on the robustness of the Sine-Gordon transition and the effects of quasidisorder and lattice depth.

Contribution

It provides a detailed numerical analysis of the Sine-Gordon transition in bosonic systems within bichromatic optical lattices, demonstrating the transition's robustness and the role of holes in the regime.

Findings

The Sine-Gordon transition is robust against quasidisorder introduced by an incommensurate secondary lattice.

Properties like correlation functions do not change with the secondary lattice depth in weak lattices.

Holes significantly influence the response of properties to interaction strength changes in the Sine-Gordon regime.

Abstract

The properties of interacting bosons in a weak, one-dimensional, and bichromatic optical with a rational ratio of the constituting wavelengths $\lambda_1$ and $\lambda_2$ are numerically examined along a broad range of the Lieb-Liniger interaction parameter $\gamma$ passing through the Sine-Gordon transition. It is argued that there should not be much difference in the results between those due to an irrational ratio $\lambda_1/\lambda_2$ and due to a rational approximation of the latter. For a weak bichromatic optical lattice, it is chiefly demonstrated that this transition is robust against the introduction of quasidisorder via a weaker, secondary, and incommensurate optical lattice superimposed on the primary one. The properties, such as the correlation function, Matsubara Green's function, and the single-particle density matrix, do not respond to changes in the depth of the secondary optical lattice $V_1$. For a stronger bichromatic optical lattice, however, a response is observed because of changes in $V_1$. It is found accordingly, that holes in the SG regime play an important role in the response of properties to changes in $\gamma$. The continuous-space worm algorithm Monte Carlo method [Boninsegni \ea, Phys. Rev. E $\mathbf{74}$, 036701 (2006)] is applied for the present examination. It is found that the worm algorithm is able to reproduce the Sine-Gordon transition that has been observed experimentally [Haller \ea, Nature $\mathbf{466}$, 597 (2010)].