Detecting delocalization-localization transitions from full density distributions

M. Hopjan,1 G. Orso,2 F. Heidrich-Meisner1

1Institut für Theoretische Physik, Georg-August-Universitat Göttingen,
Friedrich-Hund-Platz 1, 37077 Göttingen, Germany

2Laboratoire Matériaux et Phénomènes Quantiques, Université de Paris, CNRS, F-75013, Paris, France

Characterizing the delocalization transition in closed quantum systems with a many-body localized phase is a key open question in the field of nonequilibrium physics. We exploit the fact that localization of particles as realized in Anderson localization and standard many-body localization (MBL) implies Fock-space localization in single-particle basis sets characterized by a real-space index. Using a recently introduced quantitative measure for Fock-space localizationcomputed from the density distributions, the occupation distance [1], we systematically study its scaling behavior across delocalization transitions [2].

We first identify critical points from scaling collapses of numerical data with an excellent agreement with literature results for the critical disorder strengths of noninteracting fermions, such as the one-dimensional Aubry-André model and the three-dimensional Anderson model. We then observe a distinctively different scaling behavior in the case of interacting fermions with random disorder consistent with a Kosterlitz-Thouless transition. Finally, we use our measure to extract the transition point as a function of filling for interactsing fermions [2].

1. M. Hopjan and F. Heidrich-Meisner, Phys. Rev. A 101, 063617 (2020)
2. M. Hopjan, G. Orso and F. Heidrich-Meisner, arXiv:2105.10584, to appear in Phys. Rev. B

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