Particle fluctuations and the failure of simple effective models for many-body localized phases

This talk contributes to the ongoing debate whether a many-body localized phase (MBL) of a spinless fermion model with potential disorder and nearest-neighbor interactions (t-V model) exists or not. In particular, recent evidence suggests that there is a continuing subdiffusive particle transport even deep in the putative MBL phase [1, 2, 3]. Therefore, we investigate and compare the particle number fluctuations in the many-body localized phase with those in the non-interacting case (Anderson localization) and in effective models where only interaction terms diagonal in the Anderson basis are kept. We demonstrate that these types of simple effective models cannot account for the particle number fluctuations observed in the MBL phase of the microscopic model. As a consequence, it appears questionable if the microscopic model possesses an exponential number of exactly conserved local charges. If such a set of conserved local charges does not exist, then particles are expected to ultimately delocalize for any finite disorder strength.

[1] Phys. Rev. Lett. 124, 243601 (2020), [2] Phys. Rev. B 103, 024203 (2021), [3] Annals of Physics 435, 168481 (2021)