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

Abstract

We investigate and compare the particle number fluctuations in the putative many-body localized (MBL) phase of a spinless fermion model with potential disorder and nearest-neighbor interactions 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. This implies that assisted and pair hopping terms---generated when transforming the microscopic Hamiltonian into the Anderson basis---cannot be neglected. As a consequence, it appears questionable if the microscopic model possesses an exponential number of exactly conserved local charges. If such exactly conserved local charges do not exist, then particles are expected to ultimately delocalize for any finite disorder strength.

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• Cat states carrying long-range correlations in the many-body localized phase
• Contour-time approach to the disordered Bose-Hubbard model in the strong coupling regime
• Operator Growth in Disordered Spin Chains: Indications for the Absence of Many-Body Localization
• Excitation transfer in disordered spin chains with long-range exchange interactions
• Long-range resonances in quasiperiodic many-body localization
• Numerical Study of Disordered Noninteracting Chains Coupled to a Local Lindblad Bath