Mottglass phase induced by longrange correlated disorder in a onedimensional Bose gas
Abstract
We determine the phase diagram of a onedimensional Bose gas in the presence of disorder with short and longrange correlations, the latter decaying with distance as $1/x^{1+\sigma}$. When $\sigma<0$, the BerezinskiiKosterlitzThouless transition between the superfluid and the localized phase is driven by the longrange correlations and the Luttinger parameter $K$ takes the critical value $K_c(\sigma)=3/2\sigma/2$. The localized phase is a Bose glass for $\sigma>\sigma_c=3\pi^2/3\simeq 0.289868$, and a Mott glass  characterized by a vanishing compressibility and a gapless conductivity  when $\sigma<\sigma_c$. Our conclusions, based on the nonperturbative functional renormalization group and perturbative renormalization group, are confirmed by the study of the case $\sigma=1$, corresponding to a perfectly correlated disorder in space, where the model is exactly solvable in the semiclassical limit $K\to 0^+$.
 Publication:

arXiv eprints
 Pub Date:
 July 2024
 DOI:
 10.48550/arXiv.2407.03430
 arXiv:
 arXiv:2407.03430
 Bibcode:
 2024arXiv240703430D
 Keywords:

 Condensed Matter  Quantum Gases
 EPrint:
 7+7 pages, 4 figures