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

Ducatez, Raphaël

Ducatez, Raphaël (2018), Anderson localisation for infinitely many interacting particles in Hartree-Fock theory, Journal of Spectral Theory, 8, 3, p. 1019-1050. 10.4171/JST/221

Type

Article accepté pour publication ou publié

External document link

https://hal.archives-ouvertes.fr/hal-01271084

Date

2018

Journal name

Journal of Spectral Theory

Volume

Number

Publisher

European Mathematical Society

Pages

1019-1050

Abstract (EN)

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.

Subjects / Keywords

multiscale analysis.; Hartree-Fock theory; Anderson localisation