Two interacting particles in a random potential: The bag model revisited

doi:10.1016/S0038-1098(98)00263-4

Solid State Communications

Volume 107, Issue 8, 22 July 1998, Pages 379-383

https://doi.org/10.1016/S0038-1098(98)00263-4 Get rights and content

Abstract

We investigate localization properties of two correlated electrons in a one-dimensional disordered system. The results found for the “bag model” in center-of-mass and relative coordinates are compared with those obtained earlier [Frahm et al., Europhys. Lett., 31, 1995, 169] by using particle coordinates. We show that results for the two particle localization length obtained by using the bag model depend on discretization and/or boundary conditions

References (16)

B. Kramer et al.
Reports on Progress in Physics
(1993)
S.V. Kravchenko et al.
Phys. Rev. Lett.
(1996)
K.M. Itoh
Phys. Rev. Lett.
(1996)
D.L. Shepelyansky
Phys. Rev. Lett.
(1994)
Y. Imry
Europhys. Lett.
(1995)
K. Frahm et al.
Phys. Rev. Lett.
(1996)
P. Jacquod et al.
Phys. Rev. Lett.
(1997)
K. Frahm et al.
Europhys. Lett.
(1995)

There are more references available in the full text version of this article.

Cited by (12)

Non monotonic influence of Hubbard interaction on the Anderson localization of two-electron wavepackets
2014, Physica A: Statistical Mechanics and its Applications
We show that the Hubbard-like interaction between two electrons moving in a random one-dimensional potential landscape has a non monotonic influence on the Anderson localization phenomenon. Within a tight-binding approach, we follow the time-evolution of initially localized two-electron wavepackets and compute the participation number of all two-particle eigenstates. We evidence that the coupling between bounded and unbounded two-particle states leads to an overall weakening of Anderson localization of the predominant unbounded states. However, such coupling becomes ineffective in the regime of large interaction strengths on which the energy bands corresponding to these two classes of eigenstates become quite detached. We unveil that these two competing effects are at the origin of the non monotonic influence of the inter-particle interaction on Anderson localization.
Disorder and two-particle interaction in low-dimensional quantum systems
2001, Physica E: Low-Dimensional Systems and Nanostructures
Citation Excerpt :
Consequently, we concluded [42] that the TMM, applied to the TIP problem in 1D, measures an enhancement of the localization length which is due to the finiteness of the systems considered. Although the work in Ref. [42] has been criticized [43,44], we emphasize that subsequent publications have shown [45–47] that there are no variants of TMM that reproduce Eq. (1). Furthermore, in a later numerical approach [48], based on Green function methods, Song and Oppen argue that our extrapolations for M→∞ were off by ≈11% only, whereas the original TMM of [40] deviated by about a factor of 3 [48].
We review some of the recent results on two-interacting particles (TIP) in low-dimensional disordered quantum models. Special attention is given to the mapping of the problem onto random band matrices. In particular, we construct two simple, seemingly closely related examples for which an analogous mapping leads to incorrect results. We briefly discuss possible reasons for this discrepancy based on the physical differences between the TIP problem and our examples.
Scaling the localisation lengths for two interacting particles in one-dimensional random potentials
1999, Physica A: Statistical Mechanics and its Applications
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.
Eigenfunction structure and scaling of two interacting particles in the one-dimensional Anderson model
2016, European Physical Journal B
Anti-Newtonian dynamics and self-induced Bloch oscillations of correlated particles
2014, New Journal of Physics
Quantum diffusion and scaling of localized interacting electrons
2001, Annalen der Physik (Leipzig)

View all citing articles on Scopus

View full text

Two interacting particles in a random potential: The bag model revisited

Abstract

Reports on Progress in Physics

Phys. Rev. Lett.

Phys. Rev. Lett.

Phys. Rev. Lett.

Europhys. Lett.

Phys. Rev. Lett.

Phys. Rev. Lett.

Europhys. Lett.