Münster 1997 – wissenschaftliches Programm
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TT: Tiefe Temperaturen
TT 10: Niederdimensionale Systeme, Lokalisierung
TT 10.10: Vortrag
Dienstag, 18. März 1997, 16:45–17:00, F1
No enhancement of the localization length for two interacting particles in a random potential — •R. A. R"omer and M. Schreiber — Institut f"ur Physik, Technische Universit"at Chemnitz, D-09107 Chemnitz
In one dimension (1D), bosonization of the repulsive Hubbard model in the gapless phase shows that (onsite) disorder is a relevant perturbation and the ground state corresponds to a strongly localized phase. Thus it came as a surprise, when Shepelyansky [1] recently argued that the Hubbard interaction between two particles in a random potential would reduce the localization in comparison with independent particles. We present extensive transfer matrix calculations of the two-particle localization length λ2 in dependence on disorder (W), interaction strength (U) and system size M. Using an improved transfer matrix method based on the self-averaging properties of the Lyapunov exponents, we reproduce the λ2-estimates of [2] for U=1, system size M=100, and all disorders. We find, however, that the enhancement decreases with increasing M. We also study the behavior of λ2 for U=0 and show that it is not equal to the single-particle localization length λ1 for finite M. But we recover the λ1 value in the limit M→∞. However, the enhancement λ2/λ1 also vanishes completely in this limit.
[1] D. L. Shepelyansky, Phys. Rev. Lett. 73, 2607 (1994)
[2] K. Frahm, A. Müller-Groeling, J. L. Pichard and D. Weinmann, Europhys. Lett. 31, 169 (1995)