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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 $ξ_2$ of two interacting particles in a weakly random tight binding chain is increasing unexpectedly slow relative to the single particle localization length $ξ_1$, 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 $ξ_1 = 1000$. A potential nontrivial scaling regime sets in for $ ξ_1 \approx 400$, way beyond all previous numerical attacks.