Interaction-induced connectivity of disordered two-particle states

Abstract

We study the interaction-induced connectivity in the Fock space of two particles in a disordered one-dimensional potential. Recent computational studies showed that the largest localization length ${\xi }_2$ of two interacting particles in a weakly random tight binding chain is increasing unexpectedly slow relative to the single particle localization length ${\xi }_1$, questioning previous scaling estimates. We show this to be a consequence of the approximate restoring of momentum conservation of weakly localized single particle eigenstates, and disorder-induced phase shifts for partially overlapping states. The leading resonant links appear among states which share the same energy and momentum. We substantiate our analytical approach by computational studies for up to ${\xi }_1=1000$. A potential nontrivial scaling regime sets in for ${\xi }_1\approx 400$, way beyond all previous numerical attacks.

arXiv comment5 pages, 4 figures

References in corpus (20)

• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Unbounded growth of entanglement in models of many-body localization
• Repulsively bound atom pairs in an optical lattice
• Finite temperature phase transition for disordered weakly interacting bosons in one dimension
• Fractional Bloch oscillations in photonic lattices
• Dynamics of Many-Body Localization
• Quantum Lattice Solitons
• Interaction-induced delocalization of two particles in a random potential: Scaling properties
• Scaling in Interaction-Assisted Coherent Transport
• Scaling and the center of band anomaly in a one-dimensional Anderson model with diagonal disorder
• Statistics of wave interactions in nonlinear disordered systems
• Realization of Discrete Quantum Billiard in 2D Optical Lattices
• Two interacting particles in a random potential
• Quantum chaotic subdiffusion in random potentials
• Interaction induced delocalization of two particles: large system size calculations and dependence on interaction strength
• Two interacting particles in a disordered chain III: Dynamical aspects of the interplay disorder-interaction
• Probing the effects of interaction in Anderson localization using linear photonic lattices
• q-breathers in Discrete Nonlinear Schroedinger lattices
• Nonlinear Lattice Waves in Random Potentials
• Enhancement of chaotic subdiffusion in disordered ladders with synthetic gauge fields

Cited by in corpus (11)

• Eigenfunction structure and scaling of two interacting particles in the one-dimensional Anderson model
• Two-walker discrete-time quantum walks on the line with percolation
• Interacting quantum walkers: Two-body bosonic and fermionic bound states
• Quantum subdiffusion with two- and three-body interactions
• Taming two interacting particles with disorder
• Mobility edge of two interacting particles in three-dimensional random potentials
• Two-body mobility edge in the Anderson-Hubbard model in three dimensions: Molecular versus scattering states
• Absence of two-body delocalization transitions in the two-dimensional Anderson-Hubbard model
• Logarithmic expansion of many-body wave packets in random potentials
• 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