Yang-Lee Edge Singularity from a Real-Space Renormalization-Group Method

The quantum one-dimensional transverse Ising model with an imaginary longitudinal field is studied at $T=0\mathrm{}$ using a real-space renormalization-group method. Evaluation is made of the real part of the ground-state longitudinal magnetization which is related to the Yang-Lee distribution of zeros of the partition function for the two-dimensional classical Ising model. The edge exponents are found as $\sigma =-0.25\mathrm{}\pm 0.05$ and $\eta =-1.0\mathrm{}\pm 0.02$, in agreement with series expansion estimates.