Multiparticle localization for disordered systems on continuous space via the fractional moment method

Abstract

We investigate spectral and dynamical localization of a quantum system of $n$ particles on ${\mathbb{R}}^d$ which are subject to a random potential and interact through a pair potential which may have infinite range. We establish two conditions which ensure spectral and dynamical localization near the bottom of the spectrum of the $n$-particle system: i)localization is established in the regime of weak interactions supposing one-particle localization, and ii)localization is also established under a Lifshitz-tail type condition on the sparsity of the spectrum. In case of polynomially decaying interactions, we provide an upper bound on the number of particles up to which these conditions apply.

References in corpus (3)

• Eigenfunctions in a two-particle Anderson tight binding model
• A Wegner estimate for multi-particle random Hamiltonians
• Disordered Bose Einstein Condensates with Interaction in One Dimension

Cited by in corpus (11)

• On Many-Body Localization for Quantum Spin Chains
• Localization in an interacting quasi-periodic fermionic chain
• Characterization of the metal-insulator transport transition for the two-particle Anderson model
• Exponential scaling limit of the single-particle Anderson model via adaptive feedback scaling
• Exponential decay of eigenfunctions in a continuous multi-particle Anderson model with sub-exponentially decaying interaction
• Universality of smoothness of Density of States in arbitrary higher-dimensional disorder under non-local interactions I. From Viéte--Euler identity to Anderson localization
• An eigensystem approach to Anderson localization for multi-particle systems
• Comprehensive proofs of localization in Anderson models with interaction. I. Two-particle localization estimates
• Density of States under non-local interactions III. N-particle Bernoulli--Anderson model
• Efficient Anderson localization bounds for large multi-particle systems
• Efficient localization bounds in a continuous multi-particle Anderson model with long-range interaction