Numerical results for two interacting particles in a random environment

Abstract

Much evidence has been collected to date which shows that repulsive electronelectron interaction can lead to the formation of particle pairs in a one-dimensional random energy landscape. The localization length λ2 of these pair states is finite, but larger than the localization length λ1 of the individual particles. After a short review of previous work, we present numerical evidence for this effect based on an analysis of the interaction matrix elements and an application of the decimation method. The results based on the decimation method for a two-dimensional disordered medium support the localization-delocalization transition of pair states predicted recently.

Numerical Investigations of Scaling at the Anderson Transition

“…with the SP localization length λ 1 ∝ exp(t 2 /W 2 ) in 2D [36]. We found [150] that the enhancement is even stronger and as shown in Fig. 6 the scaling curves for U ≥ 0.5 have two branches indicating a transition of TIP states from localized to delocalized behavior [151].…”

“…In Ref. [150] we have employed the decimation method for TIP in quasi-1D strips of fixed length L and small cross-section M < L at E = 0. Analytical considerations for 2D [138] predict that the enhancement of λ 2 at E = 0 should be…”

Two-body mobility edge in the Anderson-Hubbard model in three dimensions: Molecular versus scattering states

“…In Ref.s [55,56] it was argued that all two-particle states remain localized in one and two dimensions (although the pair localization length can be extremely large), whereas in three dimensions an Anderson transition to a diffusive phase could occur even when all single-particle states are localized. These claims are in stark contrast with subsequent numerical works [57,58], providing evidence of 2D metal-insulator transitions of the pair induced by the Hubbard interactions (although finite-size effects can be an important issue).…”

Two-body mobility edge in the Anderson-Hubbard model in three dimensions: Molecular versus scattering states

“…[72,73] it was argued that all two-particle states remain localized in one and two dimensions (although the pair localization length can be extremely large), whereas in three dimensions an Anderson transition to a diffusive phase could occur even when all single-particle states are localized. These claims are in clear contrast with subsequent numerical works [74,75], providing evidence of 2D metal-insulator transitions of the pair induced by the Hubbard interactions (although finite-size effects can be an important issue).…”