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Title: Kosterlitz-Thouless scaling at many-body localization phase transitions

Abstract

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 lengthscale 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. In conclusion, 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 withmore » a critical exponent α c = 2, and continuously varying exponents in the MBL phase consistent with the KT picture.« less

Authors:
 [1];  [2];  [3];  [4];  [5]
  1. Flatiron Institute, New York, NY (United States)
  2. Univ. de Geneve, Geneve (Switzerland); IST Austria, Klosterneuburg (Austria)
  3. Univ. of Oxford, Oxford (United Kingdom)
  4. IST Austria, Klosterneuburg (Austria)
  5. Univ. of Massachusetts, Amherst, MA (United States)
Publication Date:
Research Org.:
Univ. of Massachusetts, Amherst, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE
OSTI Identifier:
1502413
Alternate Identifier(s):
OSTI ID: 1546188
Grant/Contract Number:  
SC0019168
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 99; Journal Issue: 9; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Dumitrescu, Philipp T., Goremykina, Anna, Parameswaran, Siddharth A., Serbyn, Maksym, and Vasseur, Romain. Kosterlitz-Thouless scaling at many-body localization phase transitions. United States: N. p., 2019. Web. doi:10.1103/PhysRevB.99.094205.
Dumitrescu, Philipp T., Goremykina, Anna, Parameswaran, Siddharth A., Serbyn, Maksym, & Vasseur, Romain. Kosterlitz-Thouless scaling at many-body localization phase transitions. United States. doi:10.1103/PhysRevB.99.094205.
Dumitrescu, Philipp T., Goremykina, Anna, Parameswaran, Siddharth A., Serbyn, Maksym, and Vasseur, Romain. Fri . "Kosterlitz-Thouless scaling at many-body localization phase transitions". United States. doi:10.1103/PhysRevB.99.094205.
@article{osti_1502413,
title = {Kosterlitz-Thouless scaling at many-body localization phase transitions},
author = {Dumitrescu, Philipp T. and Goremykina, Anna and Parameswaran, Siddharth A. and Serbyn, Maksym and Vasseur, Romain},
abstractNote = {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 lengthscale 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. In conclusion, 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.},
doi = {10.1103/PhysRevB.99.094205},
journal = {Physical Review B},
number = 9,
volume = 99,
place = {United States},
year = {2019},
month = {3}
}

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Works referenced in this record:

Ordering, metastability and phase transitions in two-dimensional systems
journal, April 1973

  • Kosterlitz, J M; Thouless, D J
  • Journal of Physics C: Solid State Physics, Vol. 6, Issue 7, p. 1181-1203
  • DOI: 10.1088/0022-3719/6/7/010