arXiv:cond-mat/9612034

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

Rudolf A. Römer, Michael Schreiber

Published Dec 3, 1996• 0 citations

Abstract

We study two interacting particles in a random potential chain by means of the transfer matrix method. The dependence of the two-particle localization length $λ_2$ on disorder and interaction strength is investigated. Our results demonstrate that the recently proposed enhancement of $λ_2$ as compared to the results for single particles is entirely due to the finite size of the systems considered. This is shown for a Hubbard-like onsite interaction and also a long-range interaction.

DOI: 10.48550/arxiv.cond-mat/9612034

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arXiv:cond-mat/9612034

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

Rudolf A. Römer, Michael Schreiber

Published Dec 3, 1996• 0 citations

arXiv HTML PDF

Abstract

We study two interacting particles in a random potential chain by means of the transfer matrix method. The dependence of the two-particle localization length

λ_2

on disorder and interaction strength is investigated. Our results demonstrate that the recently proposed enhancement of

λ_2

as compared to the results for single particles is entirely due to the finite size of the systems considered. This is shown for a Hubbard-like onsite interaction and also a long-range interaction.

DOI: 10.48550/arxiv.cond-mat/9612034

Related papers

No Enhancement of the Localization Length for Two Interacting Particles in a Random Potential

Rudolf A. Römer, Michael Schreiber

We study two interacting particles in a random potential chain by means of the transfer matrix method. The dependence of the two-particle localization length ${\ensuremath{\lambda}}_{2}$ on disorder and interaction strength is investigated. Our results demonstrate that the recently proposed enhancement of ${\ensuremath{\lambda}}_{2}$ as compared to the results for single particles is entirely due to the finite size of the systems considered. This is shown for a Hubbard-like on site interaction and also a long-range interaction.We study two interacting particles in a random potential chain by means of the transfer matrix method. The dependence of the two-particle localization length ${\ensuremath{\lambda}}_{2}$ on disorder and interaction strength is investigated. Our results demonstrate that the recently proposed enhancement of ${\ensuremath{\lambda}}_{2}$ as compared to the results for single particles is entirely due to the finite size of the systems considered. This is shown for a Hubbard-like on site interaction and also a long-range interaction.

Physical Review LettersJan 20, 199766 citations

Localization of two interacting particles in a one-dimensional random potential

Pil Hun Song, Doochul Kim

We investigate the localization of two interacting particles in a one-dimensional random potential. Our definition of the two-particle localization length, \ensuremath{\xi}, is the same as that of von Oppen et al. [Phys. Rev. Lett. 76, 491 (1996)]. \ensuremath{\xi}'s for chains of finite lengths are calculated numerically using the recursive Green's function method for several values of the strength of the disorder, $W,$ and the strength of interaction, $U.$ When $U=0,$ \ensuremath{\xi} approaches a value larger than half the single-particle localization length as the system size tends to infinity and behaves as $\ensuremath{\xi}\ensuremath{\sim}{W}^{\ensuremath{-}{\ensuremath{\nu}}_{0}}$ for small $W$ with ${\ensuremath{\nu}}_{0}=2.1\ifmmode\pm\else\textpm\fi{}0.1.$ When $U\ensuremath{\ne}0,$ we use the finite size scaling ansatz and find the relation $\ensuremath{\xi}\ensuremath{\sim}{W}^{\ensuremath{-}\ensuremath{\nu}}$ with $\ensuremath{\nu}=2.9\ifmmode\pm\else\textpm\fi{}0.2.$ Moreover, data show the scaling behavior $\ensuremath{\xi}\ensuremath{\sim}{W}^{\ensuremath{-}{\ensuremath{\nu}}_{0}}g(b|U|{/W}^{\ensuremath{\Delta}})$ with $\ensuremath{\Delta}=4.0\ifmmode\pm\else\textpm\fi{}0.5.$We investigate the localization of two interacting particles in a one-dimensional random potential. Our definition of the two-particle localization length, \ensuremath{\xi}, is the same as that of von Oppen et al. [Phys. Rev. Lett. 76, 491 (1996)]. \ensuremath{\xi}'s for chains of finite lengths are calculated numerically using the recursive Green's function method for several values of the strength of the disorder, $W,$ and the strength of interaction, $U.$ When $U=0,$ \ensuremath{\xi} approaches a value larger than half the single-particle localization length as the system size tends to infinity and behaves as $\ensuremath{\xi}\ensuremath{\sim}{W}^{\ensuremath{-}{\ensuremath{\nu}}_{0}}$ for small $W$ with ${\ensuremath{\nu}}_{0}=2.1\ifmmode\pm\else\textpm\fi{}0.1.$ When $U\ensuremath{\ne}0,$ we use the finite size scaling ansatz and find the relation $\ensuremath{\xi}\ensuremath{\sim}{W}^{\ensuremath{-}\ensuremath{\nu}}$ with $\ensuremath{\nu}=2.9\ifmmode\pm\else\textpm\fi{}0.2.$ Moreover, data show the scaling behavior $\ensuremath{\xi}\ensuremath{\sim}{W}^{\ensuremath{-}{\ensuremath{\nu}}_{0}}g(b|U|{/W}^{\ensuremath{\Delta}})$ with $\ensuremath{\Delta}=4.0\ifmmode\pm\else\textpm\fi{}0.5.$

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arXiv:1908.06643Physical review. B./Physical review. BDec 16, 201910 citations

We study two interacting particles in a random potential chain by means of the transfer matrix method. The dependence of the two-particle localization length

λ_2

on disorder and interaction strength is investigated. Our results demonstrate that the recently proposed enhancement of

λ_2

as compared to the results for single particles is entirely due to the finite size of the systems considered. This is shown for a Hubbard-like onsite interaction and also a long-range interaction.

W,

and the strength of interaction,

U.

When

U=0,

\ensuremath{\xi} approaches a value larger than half the single-particle localization length as the system size tends to infinity and behaves as $\ensuremath{\xi}\ensuremath{\sim}{W}^{\ensuremath{-}{\ensuremath{\nu}}_{0}}$ for small

W

with ${\ensuremath{\nu}}_{0}=2.1\ifmmode\pm\else\textpm\fi{}0.1.$ When $U\ensuremath{\ne}0,$ we use the finite size scaling ansatz and find the relation $\ensuremath{\xi}\ensuremath{\sim}{W}^{\ensuremath{-}\ensuremath{\nu}}$ with $\ensuremath{\nu}=2.9\ifmmode\pm\else\textpm\fi{}0.2.$ Moreover, data show the scaling behavior $\ensuremath{\xi}\ensuremath{\sim}{W}^{\ensuremath{-}{\ensuremath{\nu}}_{0}}g(b|U|{/W}^{\ensuremath{\Delta}})$ with $\ensuremath{\Delta}=4.0\ifmmode\pm\else\textpm\fi{}0.5.$

N=20\phantom{\rule{0.16em}{0ex}}000

) and disorder strengths (down to

W=0.5

). We vary the energy

E

and the on-site interaction strength

u

. At a given disorder strength, the largest enhancement of ${\ensuremath{\xi}}_{2}$ occurs for

u

of the order of the single-particle bandwidth and for two-particle states with energies at the center of the spectrum,

E=0

. We observe a crossover in the scaling of ${\ensuremath{\xi}}_{2}$ with the single-particle localization length ${\ensuremath{\xi}}_{1}$ into the asymptotic regime for ${\ensuremath{\xi}}_{1}>100$ (

W<1.0

). This happens due to the recovery of translational invariance and momentum conservation rules in the matrix elements of interconnected Fock eigenstates for

u=0

. The entrance into the asymptotic scaling is manifested through a nonlinear scaling function ${\ensuremath{\xi}}_{2}/{\ensuremath{\xi}}_{1}=F(u{\ensuremath{\xi}}_{1})$.