Taming two interacting particles with disorder

Abstract

We compute the scaling properties of the localization length ${\xi }_2$ of two interacting particles in a one-dimensional chain with diagonal disorder, and the connectivity properties of the Fock states. We analyze record large system sizes (up to $N=20000$) 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 ${\xi }_2$ occurs for $u$ of the order of the single particle band width, and for two-particle states with energies at the center of the spectrum, $E=0$. We observe a crossover in the scaling of ${\xi }_2$ with the single particle localization length ${\xi }_1$ into the asymptotic regime for ${\xi }_1>100$ ($W<1.0$). 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 ${\xi }_2/{\xi }_1=F(u{\xi }_1)$.

arXiv comment7 pages, 8 figures

References in corpus (18)

• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Interaction-induced delocalization of two particles in a random potential: Scaling properties
• Scaling in Interaction-Assisted Coherent Transport
• Variable range hopping and quantum creep in one dimension
• Short-Range Interactions and Scaling Near Integer Quantum Hall Transitions
• Coherent propagation of interacting particles in a random potential: the Mechanism of enhancement
• Two interacting particles in a random potential
• Fluctuation-Stimulated Variable-Range Hopping
• Interaction induced delocalization of two particles: large system size calculations and dependence on interaction strength
• Two interacting particles in a disordered chain II: Critical statistics and maximum mixing of the one body states
• Two interacting particles in a disordered chain III: Dynamical aspects of the interplay disorder-interaction
• Eigenfunction structure and scaling of two interacting particles in the one-dimensional Anderson model
• Localization of Two Interacting Particles in One-Dimensional Random Potential
• Breit-Wigner width for two interacting particles in one-dimensional random potential
• Surface plasmon in 2D Anderson insulator with interactions
• Interaction-induced connectivity of disordered two-particle states
• Two interacting particles in a random potential: The random matrix model revisited
• Mobility edge of two interacting particles in three-dimensional random potentials

Cited by in corpus (9)

• Interplay of disorder and interactions in a flat-band supporting diamond chain
• Multifractality of correlated two-particle bound states in quasiperiodic chains
• Absence of two-body delocalization transitions in the two-dimensional Anderson-Hubbard model
• Localization of Pairs in One-Dimensional Quasicrystals with Power-Law Hopping
• Two-body mobility edge in the Anderson-Hubbard model in three dimensions: Molecular versus scattering states
• Logarithmic expansion of many-body wave packets in random potentials
• Two-body metal-insulator transitions in the Anderson-Hubbard model
• Universal fluctuations of localized two interacting particles in one dimension
• 2D Anderson Localization and KPZ sub-Universality Classes : sensitivity to boundary conditions and insensitivity to symmetry classes