# Many-body localization phase transition: A simplified strong-randomness approximate renormalization group

## Author(s): Zhang, Liangsheng; Zhao, Bo; Devakul, Trithep; Huse, David A

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 Abstract: We present a simplified strong-randomness renormalization group (RG) that captures some aspects of the many-body localization (MBL) phase transition in generic disordered one-dimensional systems. This RG can be formulated analytically and is mathematically equivalent to a domain coarsening model that has been previously solved. The critical fixed-point distribution and critical exponents (that satisfy the Chayes inequality) are thus obtained analytically or to numerical precision. This reproduces some, but not all, of the qualitative features of the MBL phase transition that are indicated by previous numerical work and approximate RG studies: our RG might serve as a “zeroth-order” approximation for future RG studies. One interesting feature that we highlight is that the rare Griffiths regions are fractal. For thermal Griffiths regions within the MBL phase, this feature might be qualitatively correctly captured by our RG. If this is correct beyond our approximations, then these Griffiths effects are stronger than has been previously assumed. Publication Date: Jun-2016 Electronic Publication Date: 1-Jun-2016 Citation: Zhang, Liangsheng, Zhao, Bo, Devakul, Trithep, Huse, David A. (2016). Many-body localization phase transition: A simplified strong-randomness approximate renormalization group. Physical Review B, 93 (22), 10.1103/PhysRevB.93.224201 DOI: doi:10.1103/PhysRevB.93.224201 ISSN: 2469-9950 EISSN: 2469-9969 Type of Material: Journal Article Journal/Proceeding Title: Physical Review B Version: Author's manuscript