Renormalization-group study of the many-body localization transition in one dimension

Abstract

Using a new approximate strong-randomness renormalization group (RG), we study the many-body localized (MBL) phase and phase transition in one-dimensional quantum systems with short-range interactions and quenched disorder. Our RG is built on those of Zhang $\text{et al.}$ [1] and Goremykina $\text{et al.}$ [2], which are based on thermal and insulating blocks. Our main addition is to characterize each insulating block with two lengths: a physical length, and an internal decay length $\zeta$ for its effective interactions. In this approach, the MBL phase is governed by a RG fixed line that is parametrized by a global decay length $\tilde{\zeta }$, and the rare large thermal inclusions within the MBL phase have a fractal geometry. As the phase transition is approached from within the MBL phase, $\tilde{\zeta }$ approaches the finite critical value corresponding to the avalanche instability, and the fractal dimension of large thermal inclusions approaches zero. Our analysis is consistent with a Kosterlitz-Thouless-like RG flow, with no intermediate critical MBL phase.

9 pages, 4 figures; published in Physical Review B

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• Detecting ergodic bubbles at the crossover to many-body localization using neural networks
• Catching thermal avalanches in the disordered XXZ model
• Large scale behavior of the energy spectra of the quantum random antiferromagnetic Ising chain with mixed transverse and longitudinal fields
• Characterizing the many-body localization transition through correlations
• Interacting quasiperiodic spin chains in the prethermal regime
• Anatomy of localisation protected quantum order on Hilbert space