  Although strong electronic correlations are known to be responsible for some
highly unusual behaviors of solids such as, metal--insulator transitions,
magnetism and even high--temperature superconductivity, their interplay with
recently discovered topological states of matter awaits full exploration. Here
we use a modern electronic structure method combining density functional theory
of band electrons with dynamical self-energies of strongly correlated states to
predict that two well-known phases of actinide compound UNiSn, a paramagnetic
semiconducting and antiferromagnetic metallic, correspond to Topological
Insulator (TI) and Weyl semimetal (WSM) phases of topological quantum matter.
Thus, the famous unconventional insulator-metal transition observed in UNiSn is
also a TI-to-WSM transition. Driven by a strong hybridization between U
f-electron multiplet transitions and band electrons, multiple energy gaps open
up in the single-particle spectrum whose topological physics is revealed using
the calculation of Z2 invariants in the strongly correlated regime. A
simplified physical picture of these phenomena is provided based on a periodic
Anderson model of strong correlations and multiple band inversions that occur
in this fascinating compound. Studying the topology of interacting electrons
reveals interesting opportunities for finding new exotic phase transitions in
strongly correlated systems.
