Many body localization transition with correlated disorder

Zhengyan Darius Shi; Vedika Khemani; Romain Vasseur; Sarang Gopalakrishnan

doi:10.1103/PhysRevB.106.144201

paper

Many body localization transition with correlated disorder

arXiv:2204.06017 · doi:10.1103/PhysRevB.106.144201

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 $ℓ$ . For uncorrelated randomness, the characteristic scale for these fluctuations is $ℓ$ ; more generally they scale as $ℓ^{γ}$ . We discuss both positively correlated disorder ( $1/2 < γ < 1$ ) and anticorrelated, or "hyperuniform," disorder ( $γ < 1/2$ ). 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.

arXiv comment25 pages, including 9 figures, 1 table, and 3 appendices (additional reference added in v2)

Many body localization transition with correlated disorder

Abstract

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