Two interacting particles in a disordered chain II: Critical statistics and maximum mixing of the one body states

Abstract

For two particles in a disordered chain of length $L$ with on-site interaction $U$, a duality transformation maps the behavior at weak interaction onto the behavior at strong interaction. Around the fixed point of this transformation, the interaction yields a maximum mixing of the one body states. When $L\approx L_1$ (the one particle localization length), this mixing results in weak chaos accompanied by multifractal wave functions and critical spectral statistics, as in the one particle problem at the mobility edge or in certain pseudo-integrable billiards. In one dimension, a local interaction can only yield this weak chaos but can never drive the two particle system to full chaos with Wigner-Dyson statistics.

Second paper of a serie of four, to appear in Eur. Phys. J

Cited by in corpus (17)

• Many body localization in Heisenberg XXZ magnet in a random field
• Critical quantum chaos and the one dimensional Harper model
• Duality Between the Weak and Strong Interaction Limits for Randomly Interacting Fermions
• Spectral properties of quantized barrier billiards
• Energy levels and their correlations in quasicrystals
• Eigenfunction structure and scaling of two interacting particles in the one-dimensional Anderson model
• Disorder and Two-Particle Interaction in Low-Dimensional Quantum Systems
• Signatures of an intermediate 2d Coulomb phase at low temperatures
• Taming two interacting particles with disorder
• Quantum chaos in quantum Turing machines
• Low rank perturbations and the spectral statistics of pseudointegrable billiards
• Evanescent wave approach to diffractive phenomena in convex billiards with corners
• Scaling the localisation lengths for two interacting particles in one-dimensional random potentials
• Magnetic Field Effect for Two Electrons in a Two Dimensional Random Potential
• 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
• Statistical properties of two-particle transmission at Anderson transition