Scaling of the Fock-space propagator and multifractality across the many-body localization transition

Jagannath Sutradhar, Soumi Ghosh, Sthitadhi Roy, David E. Logan, Subroto Mukerjee, and Sumilan Banerjee
Phys. Rev. B 106, 054203 – Published 10 August 2022

Abstract

We implement a recursive Green's function method to extract the Fock space (FS) propagator and associated self-energy across the many-body localization (MBL) transition, for one-dimensional interacting fermions in a random on-site potential. We show that the typical value of the imaginary part of the local FS self-energy, Δt, related to the decay rate of an initially localized state, acts as a probabilistic order parameter for the thermal to MBL phase transition and can be used to characterize critical properties of the transition as well as the multifractal nature of MBL states as a function of disorder strength W. In particular, we show that a fractal dimension Ds extracted from Δt jumps discontinuously across the transition, from Ds<1 in the MBL phase to Ds=1 in the thermal phase. Moreover, Δt follows an asymmetrical finite-size scaling form across the thermal-MBL transition, where a nonergodic volume in the thermal phase diverges with a Kosterlitz-Thouless–like essential singularity at the critical point Wc and controls the continuous vanishing of Δt as Wc is approached. In contrast, a correlation length (ξ) extracted from Δt exhibits a power-law divergence on approaching Wc from the MBL phase.

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  • Received 23 March 2022
  • Revised 31 July 2022
  • Accepted 1 August 2022

DOI:https://doi.org/10.1103/PhysRevB.106.054203

©2022 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jagannath Sutradhar1,*,†, Soumi Ghosh1,2,*,‡, Sthitadhi Roy2,3,4,§, David E. Logan3,5,‖, Subroto Mukerjee1,¶, and Sumilan Banerjee1,**

  • 1Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
  • 2International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
  • 3Physical and Theoretical Chemistry, Oxford University, South Parks Road, Oxford OX1 3QZ, United Kingdom
  • 4Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom
  • 5Department of Physics, Indian Institute of Science, Bangalore 560012, India

  • *These authors contributed equally to this work.
  • sjagannath@iisc.ac.in
  • soumighosh@alum.iisc.ac.in
  • §sthitadhi.roy@icts.res.in
  • david.logan@chem.ox.ac.uk
  • smukerjee@iisc.ac.in
  • **sumilan@iisc.ac.in

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Vol. 106, Iss. 5 — 1 August 2022

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