Concepts of complex partition functions and the Fisher zeros provide
intrinsic statistical mechanisms for finite temperature and real time dynamical
phase transitions. We extend the utility of these complexifications to quantum
phase transitions. We exactly identify different Fisher zeros on lines or
closed curves and elucidate their correspondence with domain-wall excitation or
confined meson for the one-dimensional transverse field Ising model. The
crossover behavior of Fisher zeros provides a fascinating picture for
criticality near the quantum phase transition, where the excitation energy
scales are quantitatively determined. We further confirm our results by tensor
network calculation and demonstrate a clear signal of deconfined meson
excitation from the breaking of the closed zero curves. Our results
unambiguously show significant features of the Fisher zeros for a quantum phase
transition and open up a new route to explore quantum criticality.Comment: 6 pages, 4 figure