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We review recent theoretical and experimental efforts aimed at the investigation of the physics of interacting disordered bosons (so-called dirty bosons) in the context of quantum magnetism. The physics of dirty bosons is relevant to a wide variety of condensed matter systems, encompassing Helium in porous media, granular superconductors and ultracold atoms in disordered optical potentials, to cite a few. Nevertheless, the understanding of the transition from a localized, Bose-glass phase to an ordered, superfluid condensate phase still represents a fundamentally open problem. Still to be constructed is also a quantitative description of the highly inhomogeneous and strongly correlated phases connected by the transition. We discuss how disordered magnetic insulators in a strong magnetic field can provide a well controlled realization of the above transition. Combining numerical simulations with experiments on real materials can shed light on some fundamental properties of the critical behavior, such as the scaling of the critical temperature to condensation close to the quantum critical point.
We demonstrate that a combination of disorder and interactions in a two-dimensional bulk topological insulator can generically drive its helical edge insulating. We establish this within the framework of helical Luttinger liquid theory and exact Emer
We develop a theory of finite-temperature momentum-resolved tunneling spectroscopy (MRTS) for disordered, interacting two-dimensional topological-insulator edges. The MRTS complements conventional electrical transport measurement in characterizing th
We study the stability of the Wilson-Fisher fixed point of the quantum $mathrm{O}(2N)$ vector model to quenched disorder in the large-$N$ limit. While a random mass is strongly relevant at the Gaussian fixed point, its effect is screened by the stron
We study the surface of a three-dimensional spin chiral $mathrm{Z}_2$ topological insulator (class CII), demonstrating the possibility of its localization. This arises through an interplay of interaction and statistically-symmetric disorder, that con
Even though no local order parameter in the sense of the Landau theory exists for topological quantum phase transitions in Chern insulators, the highly non-local Berry curvature exhibits critical behavior near a quantum critical point. We investigate