Scaling the localisation lengths for two interacting particles in one-dimensional random potentials
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)∼
ξ
2
(0
)
α(U)
with
α(U)
varying between
α(0)≈1
and
α(1)≈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.