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


  • Römer, Rudolf A
  • Leadbeater, Mark
  • Schreiber, Michael


Using a numerical decimation method, we compute the localisation length λ2 for two onsite interacting particles (TIP) in a one-dimensional random potential. We show that an interaction U>0 does lead to λ2(U)>λ2(0) for not too large U and test the validity of various proposed fit functions for λ2(U). Finite-size scaling allows us to obtain infinite sample size estimates ξ2(U) and we find that ξ2(U)∼ξ2(0)α(U) with α(U) varying between α(0)≈1 and α(1)≈1.5. We observe that all ξ2(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.

Suggested Citation

  • Römer, Rudolf A & Leadbeater, Mark & Schreiber, Michael, 1999. "Scaling the localisation lengths for two interacting particles in one-dimensional random potentials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 266(1), pages 481-485.
  • Handle: RePEc:eee:phsmap:v:266:y:1999:i:1:p:481-485
    DOI: 10.1016/S0378-4371(98)00635-9

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