Anderson localisation for infinitely many interacting particles in Hartree-Fock theory

TL;DR

This paper proves Anderson localisation for an infinite interacting particle system in Hartree-Fock theory, showing exponential localisation of eigenvectors under certain conditions involving disorder and external potentials.

Contribution

It extends Anderson localisation results to an infinite particle system within the Hartree-Fock approximation, considering interactions and external periodic potentials.

Findings

Eigenvectors are exponentially localised in the mean-field operator.

Localisation occurs across the entire spectrum or at band edges depending on disorder strength.

Results apply to systems with weak interactions and external periodic potentials.

Abstract

We prove the occurrence of Anderson localisation for a system of infinitely many particles interacting with a short range potential, within the ground state Hartree-Fock approximation. We assume that the particles hop on a discrete lattice and that they are submitted to an external periodic potential which creates a gap in the non-interacting one particle Hamiltonian. We also assume that the interaction is weak enough to preserve a gap. We prove that the mean-field operator has exponentially localised eigenvectors, either on its whole spectrum or at the edges of its bands, depending on the strength of the disorder.