2019/06/30 by Georgios Styliaris, Namit Anand, Lorenzo Campos Venuti +1 · 1 citation
Mathematics · Physics and Astronomy · #Coherence (philosophical gambling strategy) #Ergodic theory #Hamiltonian (control theory) #Infinitesimal #Mathematical analysis #Mathematics #Physics #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #cond-mat.dis-nn #quant-ph
paper · pdf · doi:10.1103/physrevb.100.224204
published as Phys. Rev. B 100, 224204 (2019) · significantly revised version
arxiv created 2019/08/29 · openalex publication_date 2019/12/18 · arxiv updated 2019/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A dynamical signature of localization in quantum systems is the absence of transport which is governed by the amount of coherence that configuration space states possess with respect to the Hamiltonian eigenbasis. To make this observation precise, we study the localization transition via quantum coherence measures arising from the resource theory of coherence. We show that the escape probability, which is known to show distinct behavior in the ergodic and localized phases, arises naturally as the average of a coherence measure. Moreover, using the theory of majorization, we argue that broad families of coherence measures can detect the uniformity of the transition matrix (between the Hamiltonian and configuration bases) and hence act as probes to localization. We provide supporting numerical evidence for Anderson and many-body localization (MBL). For infinitesimal perturbations of the Hamiltonian, the differential coherence defines an associated Riemannian metric. We show that the latter is exactly given by the dynamical conductivity, a quantity of experimental relevance which is known to have a distinctively different behavior in the ergodic and in the many-body localized phases.