Many-body localization transition with correlated disorder
Zhengyan Darius Shi, Vedika Khemani, Romain Vasseur +1 more
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 $\ensuremath{\ell}$. For uncorrelated randomness, the characteristic scale for these fluctuations is $\sqrt{\ensuremath{\ell}}$; more generally they scale as ${\ensuremath{\ell}}^{\ensuremath{\gamma}}$. We discuss both positively correlated disorder ($1/2<\ensuremath{\gamma}<1$) and anticorrelated, or ``hyperuniform,'' disorder ($\ensuremath{\gamma}<1/2$). 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 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:2204.06017•Physical review. B./Physical review. B•Oct 5, 2022•9 citations