Unusual fluid of one-dimensional disordered bosons at finite temperature

Abstract

In previous important examinations by Aleiner et al. [Nat. Phys. 6, 900 (2010)] and Michal et al. [Proc. Natl. Acad. Sci. (U.S.A.) 113, E4455 (2016)], the fluid insulator transition has been explored in one-dimensional (1D) disordered bosons by analytical methods. However, the nature of this ``fluid'' is still not quite understood. Here we shed more light on this ``fluid'' by studying its properties under changes in the average particle number $\ensuremath{\langle}N\ensuremath{\rangle}$ and temperature $T$ in the absence of superfluidity. For this purpose, the worm algorithm path-integral Monte Carlo method is utilized in the grand-canonical ensemble. A measure for the width of path fluctuations is introduced that we call ${\ensuremath{\sigma}}_{J}$. It is found that by increasing $\ensuremath{\langle}N\ensuremath{\rangle}$, ${\ensuremath{\sigma}}_{J}$ rises as the bosons become less repulsive and gain more mobility. The compressibility $\ensuremath{\chi}(\ensuremath{\mu})$, $\ensuremath{\mu}$ being the chemical potential, reveals fluid behavior at the lower $\ensuremath{\gamma}$ and a proposed Bose-glass phase at the larger $\ensuremath{\gamma}$ (the Lieb-Liniger interaction parameter). The kinetic energy ${E}_{K}$ versus $\ensuremath{\gamma}$ at various $T$ signals a transition by its convergence towards a common value. ${E}_{K}$ versus $\ensuremath{\mu}$ reveals a peculiar inversion as one goes from small to larger values of the speckle strength $\ensuremath{\langle}V\ensuremath{\rangle}$ demonstrating a complex influence of the disorder. A tipover of ${E}_{K}$ versus $\ensuremath{\gamma}$ from an increasing to a decreasing trend at the lower $\ensuremath{\gamma}$ also signals a transition. Further, Luttinger's liquid theory cannot be applied to describe 1D bosons in strong disorder at finite $T$ because of the absence of superfluidity. Moreover, $\ensuremath{\langle}V\ensuremath{\rangle}$ largely controls the behavior of $\ensuremath{\chi}(\ensuremath{\mu})$, the pair-correlation function at the origin ${g}_{2}(0)$, and ${E}_{K}$. Surprisingly, the diffusion constant ${D}_{0}$ does not obey the classical isomorphism as it rises with $T$. We also emphasize the importance of this work via its applicability to quantum wires.