No definitive evidence of spacetime supersymmetry (SUSY) that transmutes fermions into bosons and vice versa has been revealed in nature so far. One may wonder whether SUSY can be realized in quantum materials. In this talk, I shall discuss theoretically how spacetime SUSY may emerge at the boundary of topological phases such as 3D topological insulators or in the bulk of topological semimetals such as 3D Weyl semimetals. Moreover, we have performed large-scale quantum Monte Carlo simulations of various microscopic models to numerically verify such emergence of spacetime SUSY at quantum critical points. I shall further discuss experimental signatures such as critical exponents and optical conductivity which can be measured to test such emergent SUSY in candidate systems such as the surface of 3D topological insulators.
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