Probing localization properties of many-body Hamiltonians via an imaginary vector potential
Abstract
Identifying and measuring the "localization length" in many-body systems in the vicinity of a many-body localization transition is difficult. Following Hatano and Nelson, a recent paper [S. Heußen, C. D. White, and G. Refael, Phys. Rev. B 103, 064201 (2021)] introduced an "imaginary vector potential" to a disordered ring of interacting fermions, in order to define a many-body localization length (corresponding, in the noninteracting case, to the end-to-end Green's function of the Hermitian system). We extend these results, by connecting this localization length to the length scale appearing in the avalanche model of delocalization. We use this connection to derive the distribution of the localization length at the MBL transition, finding good agreement with our numerical observations. Our results demonstrate how a localization length defined as such probes the localization of the underlying ring, without the need to explicitly construct the l-bits.
Copyright and License
© 2023 American Physical Society.
Acknowledgement
L.O.B. and G.R. thank David Huse for useful discussion regarding the distinction between single and multi l-bit flips when defining A_ℓ. L.O.B. also thanks Christopher David White for his guidance and advice during the early stages of this project, as well as Dan Borgnia for useful discussions. G.R. is grateful for support from the Simons Foundation as well as support from the NSF DMR Grant No. 1839271, and from the IQIM, an NSF Physics Frontiers Center. This work was performed in part at Aspen Center for Physics, which is supported by National Science Foundation Grant No. PHY-1607611.
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Additional details
- ISSN
- 2469-9969
- Simons Foundation
- National Science Foundation
- DMR-1839271
- National Science Foundation
- PHY-1607611
- Institute for Quantum Information and Matter, California Institute of Technology
- Caltech groups
- Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics