Exact Results for One-Dimensional Disordered Bosons with Strong Repulsion

We study one-dimensional disordered bosons with strong repulsive interactions. A Bose-Fermi mapping expresses this problem in terms of noninteracting Anderson-localized fermions, whereby known results for the distribution function of the local density of states, the spectral statistics, and density-density correlations can be transferred to this new domain of applicability. We show that disorder destroys bosonic quasi-long-range order by calculating the momentum distribution, and comment on the experimental observability of these predictions in ultracold atomic gases.

Figure 1

Momentum distribution (6) for several $\Delta$ and $N=50$ rubidium atoms in a harmonic axial trap. For the disorder average, at most 300 disorder realizations were sufficient for convergence, and $L$ was chosen large enough to ensure $L$ independence. Note the linear-logarithmic scale. Inset: Zero-momentum peak as a function of disorder strength.

Figure 2

Momentum distribution on a ring for various $\Delta$, $N/L=1/2$, with $L=600$. The $\Delta =0$ result is analytical [18, 19] and shows the $p^{-1/2}$ scaling at $p\to 0$. Note the double-logarithmic scale. The inset shows that for finite $\Delta$ and $L\ge 200$, finite-size effects are negligible.