arXiv subjects

Mark Leadbeater

Publications and source records attributed to Mark Leadbeater.

3 recordsLinked to original sources

arXiv1998

Scaling the localisation lengths for two interacting particles in one-dimensional random potentials

Using a numerical decimation method, we compute the localisation length $λ_{2}$ for two onsite interacting particles (TIP) in a one-dimensional random potential. We show that an interaction $U>0$ does lead to $λ_2(U) > λ_2(0)$ for not too large $U$ and test the validity of various proposed fit functions for $λ_2(U)$. Finite-size scaling allows us to obtain infinite sample size estimates $ξ_{2}(U)$ and we find that $ ξ_{2}(U) \sim ξ_2(0)^{α(U)} $ with $α(U)$ varying between $α(0)\approx 1$ and $α(1) \approx 1.5$. We observe that all $ξ_2(U)$ 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.

cond-mat.str-el↗

arXiv1998

Formation of electron-hole pairs in a one-dimensional random environment

We study the formation of electron-hole pairs for disordered systems in the limit of weak electron-hole interactions. We find that both attractive and repulsive interactions lead to electron-hole pair states with large localization length $λ_{2}$ even when we are in this non-excitonic limit. Using a numerical decimation method to calculate the decay of the Green function along the diagonal of finite samples, we investigate the dependence of $λ_2(U)$ on disorder, interaction strength $U$ and system size. Infinite sample size estimates $ξ_{2}(U)$ are obtained by finite-size scaling. The results show a great similarity to the problem of two interacting electrons in the same random one-dimensional potential.

cond-mat.dis-nn↗

arXiv1998

Interaction-dependent enhancement of the localisation length for two interacting particles in a one-dimensional random potential

We present calculations of the localisation length, $λ_{2}$, for two interacting particles (TIP) in a one-dimensional random potential, presenting its dependence on disorder, interaction strength $U$ and system size. $λ_{2}(U)$ is computed by a decimation method from the decay of the Green function along the diagonal of finite samples. Infinite sample size estimates $ξ_{2}(U)$ are obtained by finite-size scaling. For U=0 we reproduce approximately the well-known dependence of the one-particle localisation length on disorder while for finite $U$, we find that $ ξ_{2}(U) \sim ξ_2(0)^{β(U)} $ with $β(U)$ varying between $β(0)=1$ and $β(1) \approx 1.5$. We test the validity of various other proposed fit functions and also study the problem of TIP in two different random potentials corresponding to interacting electron-hole pairs. As a check of our method and data, we also reproduce well-known results for the two-dimensional Anderson model without interaction.

cond-mat.dis-nn↗