Interaction-induced connectivity of disordered two-particle states

We study the interaction-induced connectivity in the Fock space of two particles in a disordered one-dimensional potential. Recent computational studies showed that the largest localization length $\xi_2$ of two interacting particles in a weakly random tight binding chain is increasing unexpectedly slow relative to the single particle localization length $\xi_1$, questioning previous scaling estimates. We show this to be a consequence of the approximate restoring of momentum conservation of weakly localized single particle eigenstates, and disorder-induced phase shifts for partially overlapping states. The leading resonant links appear among states which share the same energy and momentum. We substantiate our analytical approach by computational studies for up to $\xi_1 = 1000$. A potential nontrivial scaling regime sets in for $\xi_1 \approx 400$, way beyond all previous numerical attacks.