We investigate the Yang-Lee singularity in BCS superconductivity, and find
that the zeros of the partition function accumulate on the boundary of a
quantum phase transition, which is accompanied by nonunitary quantum critical
phenomena. By applying the renormalization-group analysis, we show that
Yang-Lee zeros distribute on a semicircle in the complex plane of interaction
strength for general marginally interacting systems.Comment: 5pages, 1 figure+14 pages, 5 figure