Kosterlitz-Thouless scaling at many-body localization phase transitions

Dumitrescu, Philipp T.; Goremykina, Anna; Parameswaran, Siddharth A.; Serbyn, Maksym; Vasseur, Romain

doi:10.1103/PhysRevB.99.094205

Kosterlitz-Thouless scaling at many-body localization phase transitions

Journal Article · Fri Mar 22 00:00:00 EDT 2019 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.99.094205· OSTI ID:1502413

Dumitrescu, Philipp T. ^[1]; Goremykina, Anna ^[2]; Parameswaran, Siddharth A. ^[3]; Serbyn, Maksym ^[4]; Vasseur, Romain ^[5]

Flatiron Institute, New York, NY (United States); UMass Amherst
Univ. de Geneve, Geneve (Switzerland); IST Austria, Klosterneuburg (Austria)
Univ. of Oxford, Oxford (United Kingdom)
IST Austria, Klosterneuburg (Austria)
Univ. of Massachusetts, Amherst, MA (United States)

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 α_c = 2, and continuously varying exponents in the MBL phase consistent with the KT picture.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Massachusetts, Amherst, MA (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division

Grant/Contract Number:: SC0019168

OSTI ID:: 1502413

Alternate ID(s):: OSTI ID: 1546188

Journal Information:: Physical Review B, Journal Name: Physical Review B Journal Issue: 9 Vol. 99; ISSN 2469-9950; ISSN PRBMDO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Measurement-induced criticality in random quantum circuits Jian, Chao-Ming; You, Yi-Zhuang; Vasseur, Romain Physical Review B, Vol. 101, Issue 10 https://doi.org/10.1103/physrevb.101.104302	journal	March 2020
Multiscale entanglement clusters at the many-body localization phase transition Herviou, Loïc; Bera, Soumya; Bardarson, Jens H. Physical Review B, Vol. 99, Issue 13 https://doi.org/10.1103/physrevb.99.134205	journal	April 2019
Exact solution of a percolation analog for the many-body localization transition Roy, Sthitadhi; Logan, David E.; Chalker, J. T. Physical Review B, Vol. 99, Issue 22 https://doi.org/10.1103/physrevb.99.220201	journal	June 2019
Renormalization-group study of the many-body localization transition in one dimension Morningstar, Alan; Huse, David A. Physical Review B, Vol. 99, Issue 22 https://doi.org/10.1103/physrevb.99.224205	journal	June 2019
Multifractal Scalings Across the Many-Body Localization Transition Macé, Nicolas; Alet, Fabien; Laflorencie, Nicolas Physical Review Letters, Vol. 123, Issue 18 https://doi.org/10.1103/physrevlett.123.180601	journal	October 2019
Two critical localization lengths in the Anderson transition on random graphs García-Mata, I.; Martin, J.; Dubertrand, R. Physical Review Research, Vol. 2, Issue 1 https://doi.org/10.1103/physrevresearch.2.012020	journal	January 2020
Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions Roy, Sthitadhi; Logan, David E. SciPost Physics, Vol. 7, Issue 4 https://doi.org/10.21468/scipostphys.7.4.042	journal	January 2019
Exact solution of a percolation analogue for the many-body localisation transition Roy, Sthitadhi; Logan, David E.; Chalker, J. T. arXiv https://doi.org/10.48550/arxiv.1812.05115	text	January 2018
Multifractal Scalings across the Many-Body Localization Transition Macé, Nicolas; Alet, Fabien; Laflorencie, Nicolas arXiv https://doi.org/10.48550/arxiv.1812.10283	text	January 2018
Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions Roy, Sthitadhi; Logan, David E. arXiv https://doi.org/10.48550/arxiv.1903.04851	text	January 2019
Diffusive transport in a quasiperiodic Fibonacci chain: absence of many-body localization at small interactions Varma, Vipin Kerala; Znidaric, Marko arXiv https://doi.org/10.48550/arxiv.1905.03128	text	January 2019
Measurement-induced criticality in random quantum circuits Jian, Chao-Ming; You, Yi-Zhuang; Vasseur, Romain arXiv https://doi.org/10.48550/arxiv.1908.08051	text	January 2019
Slow dynamics and strong finite-size effects in many-body localization with random and quasiperiodic potentials Weiner, Felix; Evers, Ferdinand; Bera, Soumya Universität Regensburg https://doi.org/10.5283/epub.45856	text	January 2019

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