The question of the stability of Anderson localisation (AL) against weak interactions has been raised since the early days of the field. However, despite the enormous efforts devoted to the study of the many-body localisation (MBL) phenomenon, this question has remained unanswered ever since.
In the recent Phys. Rev. Lett. 133, 116502 (2024), building on the shift-invert diagonalisation of the random field spin-1/2 XXZ chain model, J. Colbois, F. Alet and N. Laflorencie have found that below a certain disorder threshold, weak interactions necessarily lead to an ergodic instability, whereas at strong disorder the AL insulator turns directly into an MBL, in agreement with a simple interpretation of avalanche theory for the restoration of ergodicity. We further map the phase diagram for the generic model in the disorder-interaction plane. Taking advantage of the total magnetization conservation, our results reveal the remarkable behaviour of the spin-spin correlation functions: in the regime indicated as MBL by standard observables, their exponential decay undergoes an inversion of orientation 𝜉𝑧 >𝜉𝑥. We find that the longitudinal length 𝜉𝑧 is a key quantity for capturing ergodic instabilities, as it increases with system size near the thermal phase, in sharp contrast to its transverse counterpart.
