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

Sutradhar, J and Ghosh, S and Roy, S and Logan, DE and Mukerjee, S and Banerjee, S (2022) Scaling of the Fock-space propagator and multifractality across the many-body localization transition. In: Physical Review B, 106 (5).

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Official URL: https://doi.org/10.1103/PhysRevB.106.054203


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 (ζ) extracted from Δt exhibits a power-law divergence on approaching Wc from the MBL phase.

Item Type: Journal Article
Publication: Physical Review B
Publisher: American Physical Society
Additional Information: The copyright for this article belongs to the Author(s).
Keywords: Algebra; Decay (organic), Fock spaces; Greens' function method; Localisation; Many body; Multifractality; One-dimensional; Scalings; Self energy; Thermal; Thermal phase, Fractal dimension
Department/Centre: Division of Physical & Mathematical Sciences > Physics
Date Deposited: 19 Sep 2022 08:33
Last Modified: 19 Sep 2022 08:33
URI: https://eprints.iisc.ac.in/id/eprint/76590

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