Minimal model of many-body localization

We present a fully analytical description of many-body localization (MBL) transition in microscopically defined model. Its Hamiltonian is the sum one- and two-body operators, where both contributions obey maximum-entropy principle have no symmetries except Hermiticity (not even particle number conservation). These two criteria paraphrase that our system variant Sachdev-Ye-Kitaev will demonstrate how this simple zero-dimensional displays numerous features seen more complex realizations MBL. Specifically, it shows between an ergodic localized phase, nontrivial wave-function statistics indicating presence nonergodic extended states. check these phenomena by parameter-free comparison to high performance numerics for systems up N=15 fermions. In way, study becomes test bed concepts high-dimensional quantum localization, previously applied synthetic such as Cayley trees or random regular graphs. The minimal model describes which effective theory derived solved from first principles. hope developed may become stepping stone MBL systems.1 MoreReceived 29 June 2020Accepted 3 December 2020DOI:https://doi.org/10.1103/PhysRevResearch.3.013023Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasMany-body localizationTechniquesErgodic theorySachdev-Ye-Kitaev modelCondensed Matter & Materials Physics