Excitation Spectrum at the Yang-Lee Edge Singularity of the 2D Ising model

This paper studies the Yang-Lee edge singularity of 2-dimensional (2D) Ising model through a quantum spin chain. In particular, finite-size scaling measurements on the quantum spin chain are used to determine the low-lying excitation spectrum and central charge at the Yang-Lee edge singularity. The measured values are consistent with predictions for the (A4, A1) minimal conformal field theory. In 1978, Fisher[1] argued forcefully that Yang-Lee edge singularities[2, 3] are similar to ordinary critical points. Later, Cardy[4] provided another strong argument that the Yang-Lee edge singularity of the 2D Ising model is identified with the (A4, A1) minimal conformal field theory (CFT)[5, 6] of the ADE classification.[7] Cardy’s identification enables a number of CFT predictions about the Yang-Lee edge singularity of the 2D Ising model. Some of these CFT predictions have been confirmed. Using transfer matrix methods, Itzykson et al measured the central charge and exponent ν at the Yang-Lee edge singularity of the 2D Ising model.[8] Using short quantum spin chains,[9] Uzelac et al also measured the exponent ν at the Yang-Lee edge singularity of the 2D Ising model.[10] Both measurements are in agreement with predictions derived from Cardy’s identification. This article provides other measurements that can be predicted based on Cardy’s identification. The measurements provide the low-lying excitation spectrum at this Yang-Lee edge singularity of the 2D Ising model. This article also