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

Abstract

We present calculations of the localisation length, ${\lambda }_2$, for two interacting particles (TIP) in a one-dimensional random potential, presenting its dependence on disorder, interaction strength $U$ and system size. ${\lambda }_2(U)$ is computed by a decimation method from the decay of the Green function along the diagonal of finite samples. Infinite sample size estimates ${\xi }_2(U)$ 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 ${\xi }_2(U)\sim {\xi }_2(0{)}^{\beta (U)}$ with $\beta (U)$ varying between $\beta (0)=1$ and $\beta (1)\approx 1.5$. 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.

34 RevTeX 3.0 pages with 16 figures included

Cited by in corpus (19)

• Many-body localization transition in a lattice model of interacting fermions: statistics of renormalized hoppings in configuration space
• The Aharonov-Bohm effect for an exciton
• Interacting particles at a metal-insulator transition
• Magneto-transport in periodic and quasiperiodic arrays of mesoscopic rings
• Disorder effects in the two-dimensional Lieb lattice and its extensions
• Eigenfunction structure and scaling of two interacting particles in the one-dimensional Anderson model
• Disorder and Interactions in 1D Systems
• A critical Dyson hierarchical model for the Anderson localization transition
• Localization properties in Lieb lattices and their extensions
• Random elastic networks : strong disorder renormalization approach
• Disorder and Two-Particle Interaction in Low-Dimensional Quantum Systems
• Localisation and finite-size effects in graphene flakes
• Spin filter for arbitrary spins by substrate engineering
• Scaling the localisation lengths for two interacting particles in one-dimensional random potentials
• Localization of electronic states in amorphous materials: recursive Green's function method and the metal-insulator transition at E<>0
• Magnetic Field Effect for Two Electrons in a Two Dimensional Random Potential
• Numerical methods for localization
• Spectral Determinant Method for Interacting N-body Systems Including Impurities
• Statistical properties of two-particle transmission at Anderson transition