2014/08/26 by Rahul Nandkishore · 3 citations
Mathematics · Physics and Astronomy · #Delocalized electron #Geometry #Mathematics #Model Reduction and Neural Networks #Physics #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Theoretical physics #cond-mat.dis-nn #cond-mat.quant-gas #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.90.184204
published as Phys. Rev. B 90, 184204 (2014)
arxiv created 2014/08/26 · openalex publication_date 2014/11/25 · arxiv updated 2014/12/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We discuss whether localization in the two-dimensional continuum can be stable in the presence of short-range interactions. We conclude that, for an impurity model of disorder, if the system is prepared below a critical temperature T<Tc, then perturbation theory about the localized phase converges almost everywhere. As a result, the system is at least asymptotically localized and perhaps even truly many-body localized, depending on how certain rare regions behave. Meanwhile, for T>Tc, perturbation theory fails to converge, which we interpret as interaction-mediated delocalization. We calculate the boundary of the region of perturbative stability of localization in the interaction-strength-temperature plane. We also discuss the behavior in a speckle disorder (relevant for cold-atom experiments) and conclude that perturbation theory about the noninteracting phase diverges for arbitrarily weak interactions with speckle disorder, suggesting that many-body localization in the two-dimensional continuum cannot survive away from the impurity limit.