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Scaling the localisation lengths for two interacting particles in one-dimensional random potentials

Rudolf A. Roemer·Mark Leadbeater·Michael Schreiber
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Abstract

Using a numerical decimation method, we compute the localisation length $λ_{2}$ for two onsite interacting particles (TIP) in a one-dimensional random potential. We show that an interaction $U>0$ does lead to $λ_2(U) > λ_2(0)$ for not too large $U$ and test the validity of various proposed fit functions for $λ_2(U)$. Finite-size scaling allows us to obtain infinite sample size estimates $ξ_{2}(U)$ and we find that $ ξ_{2}(U) \sim ξ_2(0)^{α(U)} $ with $α(U)$ varying between $α(0)\approx 1$ and $α(1) \approx 1.5$. We observe that all $ξ_2(U)$ data can be made to coalesce onto a single scaling curve. We also present results for the problem of TIP in two different random potentials corresponding to interacting electron-hole pairs.

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Rudolf A. Roemer, Mark Leadbeater, Michael Schreiber. 1998-09-28. Scaling the localisation lengths for two interacting particles in one-dimensional random potentials. https://doi.org/10.1016/s0378-4371(98)00635-9

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