The pair localization length L2 of two interacting electrons in one-dimensional disordered systems is studied numerically. Using two direct approaches, we find L2 ∝ L α 1 , where L1 is the one-electron localization length and α ≈ 1.65. This demonstrates the enhancement effect proposed by Shepelyansky, but the value of α differs from previous estimates (α = 2) in the disorder range considered. We explain this discrepancy using a scaling picture recently introduced by Imry and taking into account a more accurate distribution than previously assumed for the overlap of one-electron wavefunctions.PACS numbers: 71.30, 72.15.R Very recently, Shepelyansky [1] considered the problem of two interacting electrons in a random potential, defined by the Schrödinger equation, U characterizes the on-site interaction and V i is a random potential distributed uniformly in the interval [−W, W ]. The indices n 1 and n 2 denote the positions of the first and the second electron, respectively. Shepelyansky proposed that, as a consequence of the interaction U , certain eigenstates extend over a range L 2 much larger than the one-particle localization length L 1 ∝ W −2 . A key quantity in the derivation of this spectacular result in one dimension is the matrix representation U of the Hubbard interaction in the disorder diagonal basis of localized oneelectron eigenstates. With R n,i the amplitude at site n of the one-particle eigenstate with energy E i we have U ij,lm = U Q ij,lm with Q ij,lm = n R n,i R n,j R n,l R n,m .(The Q ij,lm vanish unless all four eigenstates are roughly localized within the same box of size L 1 . Assuming that R n,i ∝ a n / √ L 1 inside the box, with a n a random number of order unity, and neglecting correlations among the a n at different sites n, one finds Q ≈ 1/L 3/2 1 for a typical nonvanishing matrix element. In [1], this estimate was adopted and used to reduce the original problem to a certain band matrix model, eventually giving L 2 ∝ L 2 1 . Later, Imry [2] employed the Thouless scaling block picture to reinforce, interpret and generalize this result. The key step in this approach involves the pair conductance g 2 = (U Q/δ 2 ) 2 , where δ 2 is the two-particle level spacing in a block of size L 1 and Q is evaluated between adjacent blocks. Using Q ≈ 1/L 3/2 1 as before, Imry finds that g 2 ≈ 1 on the scale L 2 ∝ L 2 1 , in agreement with Shepelyansky. As a second important result both approaches predict that the effect does not depend on the sign of U .In this letter, we confirm the enhancement effect by studying both the original model (1) for finite size samples and an infinite "bag model" with medium-range interaction. However, we find L 2 ∝ L α 1 with α ≈ 1.65 instead of α = 2 in both cases. Moreover, the sign of U is not entirely irrelevant. We suggest that the small value for α is due to a very peculiar distribution of the Q ij,lm .
