Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
1998-09-13
Eur. Phys. J. B 10, 371 (1999)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
8 pages, 5 figures, LaTeX, EPJ macro package, submitted to the European Physical Journal B
Scientific paper
10.1007/s100510050866
The localization length $L_2$ of two interacting particles in a one-dimensional disordered system is studied for very large system sizes by two efficient and accurate variants of the Green function method. The numerical results (at the band center) can be well described by the functional form $L_2=L_1[0.5+c(U) L_1]$ where $L_1$ is the one-particle localization length and the coefficient $c(U)\approx 0.074 |U|/(1+|U|)$ depends on the strength $U$ of the on-site Hubbard interaction. The Breit-Wigner width or equivalently the (inverse) life time of non-interacting pair states is analytically calculated for small disorder and taking into account the energy dependence of the one-particle localization length. This provides a consistent theoretical explanation of the numerically found $U$-dependence of $c(U)$.
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