Many body localization transition with correlated disorder

Abstract

We address the critical properties of the many-body localization (MBL) phase transition in one-dimensional systems subject to spatially correlated disorder. We consider a general family of disorder models, parameterized by how strong the fluctuations of the disordered couplings are when coarse-grained over a region of size $\ell$. For uncorrelated randomness, the characteristic scale for these fluctuations is $\sqrt{\ell }$; more generally they scale as ${\ell }^{\gamma }$. We discuss both positively correlated disorder ($1/2<\gamma <1$) and anticorrelated, or "hyperuniform," disorder ($\gamma <1/2$). We argue that anticorrelations in the disorder are generally irrelevant at the MBL transition. Moreover, assuming the MBL transition is described by the recently developed renormalization-group scheme of Morningstar \emph{et al.} [Phys. Rev. B 102, 125134, (2020)], we argue that even positively correlated disorder leaves the critical theory unchanged, although it modifies certain properties of the many-body localized phase.

25 pages, including 9 figures, 1 table, and 3 appendices (additional reference added in v2)

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