---
_id: '6174'
abstract:
- lang: eng
text: We propose a scaling theory for the many-body localization (MBL) phase transition
in one dimension, building on the idea that it proceeds via a “quantum avalanche.”
We argue that the critical properties can be captured at a coarse-grained level
by a Kosterlitz-Thouless (KT) renormalization group (RG) flow. On phenomenological
grounds, we identify the scaling variables as the density of thermal regions and
the length scale that controls the decay of typical matrix elements. Within this
KT picture, the MBL phase is a line of fixed points that terminates at the delocalization
transition. We discuss two possible scenarios distinguished by the distribution
of rare, fractal thermal inclusions within the MBL phase. In the first scenario,
these regions have a stretched exponential distribution in the MBL phase. In the
second scenario, the near-critical MBL phase hosts rare thermal regions that are
power-law-distributed in size. This points to the existence of a second transition
within the MBL phase, at which these power laws change to the stretched exponential
form expected at strong disorder. We numerically simulate two different phenomenological
RGs previously proposed to describe the MBL transition. Both RGs display a universal
power-law length distribution of thermal regions at the transition with a critical
exponent αc=2, and continuously varying exponents in the MBL phase consistent
with the KT picture.
article_number: '094205'
article_processing_charge: No
article_type: original
author:
- first_name: Philipp T.
full_name: Dumitrescu, Philipp T.
last_name: Dumitrescu
- first_name: Anna
full_name: Goremykina, Anna
last_name: Goremykina
- first_name: Siddharth A.
full_name: Parameswaran, Siddharth A.
last_name: Parameswaran
- first_name: Maksym
full_name: Serbyn, Maksym
id: 47809E7E-F248-11E8-B48F-1D18A9856A87
last_name: Serbyn
orcid: 0000-0002-2399-5827
- first_name: Romain
full_name: Vasseur, Romain
last_name: Vasseur
citation:
ama: Dumitrescu PT, Goremykina A, Parameswaran SA, Serbyn M, Vasseur R. Kosterlitz-Thouless
scaling at many-body localization phase transitions. Physical Review B.
2019;99(9). doi:10.1103/physrevb.99.094205
apa: Dumitrescu, P. T., Goremykina, A., Parameswaran, S. A., Serbyn, M., & Vasseur,
R. (2019). Kosterlitz-Thouless scaling at many-body localization phase transitions.
Physical Review B. American Physical Society. https://doi.org/10.1103/physrevb.99.094205
chicago: Dumitrescu, Philipp T., Anna Goremykina, Siddharth A. Parameswaran, Maksym
Serbyn, and Romain Vasseur. “Kosterlitz-Thouless Scaling at Many-Body Localization
Phase Transitions.” Physical Review B. American Physical Society, 2019.
https://doi.org/10.1103/physrevb.99.094205.
ieee: P. T. Dumitrescu, A. Goremykina, S. A. Parameswaran, M. Serbyn, and R. Vasseur,
“Kosterlitz-Thouless scaling at many-body localization phase transitions,” Physical
Review B, vol. 99, no. 9. American Physical Society, 2019.
ista: Dumitrescu PT, Goremykina A, Parameswaran SA, Serbyn M, Vasseur R. 2019. Kosterlitz-Thouless
scaling at many-body localization phase transitions. Physical Review B. 99(9),
094205.
mla: Dumitrescu, Philipp T., et al. “Kosterlitz-Thouless Scaling at Many-Body Localization
Phase Transitions.” Physical Review B, vol. 99, no. 9, 094205, American
Physical Society, 2019, doi:10.1103/physrevb.99.094205.
short: P.T. Dumitrescu, A. Goremykina, S.A. Parameswaran, M. Serbyn, R. Vasseur,
Physical Review B 99 (2019).
date_created: 2019-03-25T07:32:08Z
date_published: 2019-03-22T00:00:00Z
date_updated: 2023-09-05T12:11:13Z
day: '22'
department:
- _id: MaSe
doi: 10.1103/physrevb.99.094205
external_id:
arxiv:
- '1811.03103'
isi:
- '000462883200001'
intvolume: ' 99'
isi: 1
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1811.03103
month: '03'
oa: 1
oa_version: Preprint
publication: Physical Review B
publication_identifier:
eissn:
- 2469-9969
issn:
- 2469-9950
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Kosterlitz-Thouless scaling at many-body localization phase transitions
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 99
year: '2019'
...