Comment on "No enhancement of the localization length for two interacting particles in a random potential"

TL;DR

This paper challenges recent claims that the localization length of two interacting particles in a random potential does not increase with system size, providing new numerical evidence that it remains enhanced and size-independent.

Contribution

The authors present new numerical results using a Green function method that demonstrate the persistent enhancement of the two-particle localization length, countering prior extrapolation-based conclusions.

Findings

$L_2$ remains significantly enhanced for system sizes between 100 and 1000.

The localization length $L_2$ is independent of system size in the studied range.

Previous claims of vanishing enhancement are contradicted by new data.

Abstract

In a recent letter [Phys. Rev. Lett. 78, 515 (1997); cond-mat/9612034] Roemer and Schreiber report on numerical calculations that led them to conclude that the previously observed enhancement of the localization length $L_2$ of two interacting particles (TIP) vanishes in the thermodynamic limit. We point out that such a claim (i) is in conflict with the scaling theory of localization, (ii) ignores a consistent picture from a wealth of published numerical data and analytical investigations, and (iii) directly contradicts new numerical results obtained with a Green function method that is well adapted to the problem under study. The claim of Roemer and Schreiber is based on extrapolating from L<360 to infinity. Our data clearly shows the two particle localization length $L_2$ to be significantly enhanced and independent of system size between L=100 and L=1000, as expected on physical grounds.