Many-body localization transition with correlated disorder

We address the critical properties of the many-body localization (MBL) phase transition in one-dimensional systems subject to spatially correlated disorder. Rather than starting from a microscopic model, we analyze the transition within a strong-randomness renormalization group (RG) framework. We introduce disorder directly at the level of scaling variables appearing in the RG and consider a general family of spatial correlations, 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 ℓγ. 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 et al. [Phys. Rev. B 102, 125134 (2020)10.1103/PhysRevB.102.125134], we argue that even positively correlated disorder leaves the critical theory unchanged, although it modifies certain properties of the many-body localized phase.