Scaling theory of few-particle delocalization

We develop a scaling theory of interaction-induced delocalization few-particle states in disordered quantum systems. In the absence interactions, all single-particle are localized $d<3$, while $d \geq 3$ there is critical disorder below which delocalized. hypothesize that such transition occurs for $n$-particle bound $d$ dimensions when $d+n\geq 4$. Exact calculations disorder-averaged Greens functions support our hypothesis. particular, we show $3$-particle $d=1$ with nearest-neighbor repulsion will delocalize $W_c \approx 1.4t$ and localization length exponent $\nu = 1.5 \pm 0.3$. The can be understood by means mapping onto non-interacting problem symplectic symmetry. discuss importance this result many-body delocalization, how few-body probed cold atom experiments.