A T=0 real‐space renormalization‐group method is presented and applied to the quantum 1D transverse field Ising model in the presence of a longitudinal field. This is an indirect way to study the equation of state of the equivalent 2D classical Ising model at finite temperature. When the longitudinal field is purely imaginary we obtain a new critical behavior which is related to the Yang‐Lee edge singularity of the corresponding classical model. We extract the edge exponent &sgr; in agreement with previous series expansion estimates.