  We study the effect of electron interaction in an electronic system with a
high-order Van Hove singularity, where the density of states shows a power-law
divergence. Owing to scale invariance, we perform a renormalization group (RG)
analysis to find a nontrivial metallic behavior where various divergent
susceptibilities coexist but no long-range order appears. We term such a
metallic state as a supermetal. Our RG analysis reveals noninteracting and
interacting fixed points, which draws an analogy to the $\phi^4$ theory. We
further present a finite anomalous dimension at the interacting fixed point by
a controlled RG analysis, thus establishing an interacting supermetal as a
non-Fermi liquid.
