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

Abstract

Using a numerical decimation method, we compute the localisation length ${\lambda }_2$ for two onsite interacting particles (TIP) in a one-dimensional random potential. We show that an interaction $U>0$ does lead to ${\lambda }_2(U)>{\lambda }_2(0)$ for not too large $U$ and test the validity of various proposed fit functions for ${\lambda }_2(U)$. Finite-size scaling allows us to obtain infinite sample size estimates ${\xi }_2(U)$ and we find that ${\xi }_2(U)\sim {\xi }_2(0{)}^{\alpha (U)}$ with $\alpha (U)$ varying between $\alpha (0)\approx 1$ and $\alpha (1)\approx 1.5$. We observe that all ${\xi }_2(U)$ 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.

proceedings of "Percolation98", 5 Elsart pages with 5 figures to be published in Physica A

References in corpus (2)

• Interaction-dependent enhancement of the localisation length for two interacting particles in a one-dimensional random potential
• Two interacting particles in a disordered chain II: Critical statistics and maximum mixing of the one body states

Cited by in corpus (1)

• Disorder and Two-Particle Interaction in Low-Dimensional Quantum Systems