Regular Article

Role of the second nearest-neighbor hoppings in a disordered Bose–Hubbard Hamiltonian in the Many-Body Localization

Atoms and Molecules Laboratory, Centre for Atomic Molecular Physics and Quantum Optics (CEPAMOQ), Faculty of Science, University of Douala, P.O. Box 8580 Douala, Cameroon

^a e-mail: bouricelsus@yahoo.fr

Received: 27 March 2020
Received in final form: 28 July 2020
Accepted: 13 August 2020
Published online: 14 September 2020

Abstract

We investigate in this work the survival of the Many-Body Localization in a discrete disordered Bose–Hubbard Hamiltonian when the second nearest-neighbor hoppings are taken into account. We consider small size systems of cold atoms located in a one-dimensional disorder optical lattices. Considering the disorder strength, we focus our attention on the spectral properties of the quantum many-body system such as the level-spacing statistics. As a result, the shapes of the probability distributions show that the systems undergo a delocalized and a localized regimes for low and high disorder strength respectively. This result is reinforced by the mean-square deviation studies.