A finite-temperature phase transition for disordered weakly interacting bosons in one dimension

It is commonly accepted that there are no phase transitions in one-dimensional systems at a finite temperature, because long-range correlations are destroyed by thermal fluctuations. Here we show theoretically that the one-dimensional gas of short-range interacting bosons in the presence of disorder can undergo a finite-temperature phase transition between two distinct states: fluid and insulator. Neither of these states has long-range spatial correlations, but this is a true, albeit non-conventional, phase transition, because transport properties are singular at the transition point. In the fluid phase, mass transport is possible, whereas in the insulator phase it is completely blocked even at finite temperatures. This study thus provides insight into how the interaction between disordered bosons influences their Anderson localization. This question, first raised for electrons in solids, is now crucial for the studies of atomic bosons, where recent experiments have demonstrated Anderson localization in expanding dilute quasi-one-dimensional clouds.