Scaling theory of few-particle delocalization

We develop a scaling theory of interaction-induced delocalization of few-particle states in disordered quantum systems. In the absence of interactions, all single-particle states are localized in d < 3, while in d 3 there is a critical disorder below which states are delocalized. We hypothesize that such a delocalization transition occurs for n-particle bound states in d dimensions when d + n 4. Exact calculations of disorder-averaged n-particle Green's functions support our hypothesis. In particular, we show that three-particle states in d = 1 with nearest-neighbor repulsion will delocalize with Wc approximate to 1.4t and with localization length critical exponent nu = 1.5 +/- 0.3. The delocalization transition can be understood by means of a mapping onto a noninteracting problem with symplectic symmetry. We discuss the importance of this result for many-body delocalization, and how few-body delocalization can be probed in cold atom experiments.

Automated summary

This study presents a scaling theory of interaction-induced delocalization of few-particle states in disordered quantum systems, proposing a delocalization transition condition and providing calculations to support the hypothesis. It discusses the significance of delocalization of multi-particle states under specific conditions and the delocalization transition.