Finite-Temperature Disordered Bosons in Two Dimensions

We study phase transitions in a two dimensional weakly interacting Bose gas in a random potential at finite temperatures. We identify superfluid, normal fluid, and insulator phases and construct the phase diagram. At $T=0$ one has a tricritical point where the three phases coexist. The truncation of the energy distribution at the trap barrier, which is a generic phenomenon in cold atom systems, limits the growth of the localization length and in contrast to the thermodynamic limit the insulator phase is present at any temperature.

Figure 1

Phase diagram for 2D weakly interacting disordered bosons in terms of the dimensionless disorder strength ${\epsilon }_{*}/ng$ and temperature $T/ng$ for $T_d/ng=11$, with $C=1$ and $f(0.54)=0.27$. The MBLDT border between the insulator and normal fluid follows almost a horizontal line ${\epsilon }_{*}/ng\simeq 0.54$ until the disorder approaches ${\epsilon }_{*}/ng=2T/ng$. The line of the MBLDT is obtained with the distribution function truncated at ${\epsilon }_b=1.21ng+5T$. The solid part of the normal fluid-superfluid line is the result of Eq. (23), and the dashed part is our expectation of how it continues at $T\lesssim ng$ until it reaches the tricritical point at $T=0$ (red point).