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]

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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)

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.

• Research Organization: Univ. of Massachusetts, Amherst, MA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE
• Grant/Contract Number: SC0019168
• OSTI ID: 1502413
• Alternate ID(s): OSTI ID: 1546188
• Journal Information: Physical Review B, Vol. 99, Issue 9; ISSN 2469-9950
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

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