Anderson transition on the Bethe lattice: an approach with real energies

Year: 2020

Authors: Parisi G., Pascazio S., Pietracaprina F., Ros V., Scardicchio A.

Autors Affiliation: Univ Roma La Sapienza, Dipartimento Fis, Piazzale Aldo Moro 2, I-00185 Rome, Italy; CNR, INFM, Ctr Stat Mech & Complex SMC, I-00185 Rome, Italy; INFN, Sez Roma, I-00185 Rome, Italy; Univ Bari, Dipartimento Fis, I-70126 Bari, Italy; Univ Bari, MECENAS, I-70126 Bari, Italy; INFN, Sez Bari, I-70126 Bari, Italy; CNR, INO, Ist Nazl Ottica, I-50125 Florence, Italy; Univ Toulouse, CNRS, UPS, Lab Phys Theor,IRSAMC, Toulouse, France; Univ Paris Diderot, Sorbonne Univ, Univ PSL,ENS,CNRS, Lab Phys,Ecole Normale Super,Sorbonne Paris Cite, Paris, France; Abdus Salam Int Ctr Theoret Phys, Str Costiera 11, I-34151 Trieste, Italy; INFN, Sez Trieste, Via Valerio 2, I-34127 Trieste, Italy.

Abstract: We study the Anderson model on the Bethe lattice by working directly with propagators at real energies E. We introduce a novel criterion for the localization-delocalization transition based on the stability of the population of the propagators, and show that it is consistent with the one obtained through the study of the imaginary part of the self-energy. We present an accurate numerical estimate of the transition point, as well as a concise proof of the asymptotic formula for the critical disorder on lattices of large connectivity, as given in Anderson (1958 Phys. Rev. 109 1492-505). We discuss how the forward approximation used in analytic treatments of localization problems fits into this scenario and how one can interpolate between it and the correct asymptotic analysis.

Journal/Review: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

Volume: 53 (1)      Pages from: 14003-1  to: 14003-28

More Information: The authors would like to thank V Kravtsov, L Ioffe, A Mirlin and K Tikhonov for interesting discussions. FP thanks G Lemarie for discussions and acknowledges the support of the project THERMOLOC ANR-16-CE30-0023-02 of the French National Research Agency (ANR). VR acknowledges the support of the Simons Foundation collaboration Cracking the Glass Problem (No. 454935 to G Biroli). SP is partially supported by Istituto Nazionale di Fisica Nucleare (INFN) through the project ’QUANTUM’. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement 694925).
KeyWords: Anderson model; Bethe lattice; localization transition
DOI: 10.1088/1751-8121/ab56e8

Citations: 36
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