Pseudo-Yang-Lee Edge Singularity Critical Behavior in a Non-Hermitian Ising Model.

Area of Science:

• Condensed matter physics
• Quantum phase transitions
• Statistical mechanics

Background:

• The Yang-Lee edge singularity (YLES) is a critical phenomenon in statistical mechanics.
• Understanding critical behaviors near YLES is crucial for characterizing phase transitions.
• Traditional order parameters often diverge at singularity points.

Purpose of the Study:

• To introduce and investigate a new order parameter, M, for quantum phase transitions.
• To explore the critical behaviors around the Yang-Lee edge singularity (YLES).
• To assess the applicability of scaling theories in describing the behavior of M.

Main Methods:

• Study of a one-dimensional transverse field Ising model with an imaginary longitudinal field.
• Introduction of a novel order parameter, M.
• Numerical investigation across different critical regions: (1+1)D ferromagnetic-paramagnetic phase transition, (0+1)D YLES, and (1+1)D YLES.
• Analysis of static and driven dynamics of the order parameter M.

Main Results:

• A new order parameter M was introduced, which does not diverge at the YLES point, termed pseudo-YLES.
• The scaling theories for (1+1)D ferromagnetic-paramagnetic phase transition, (0+1)D YLES, and (1+1)D YLES were found applicable to M.
• M demonstrates finite values around YLES, suggesting it is a suitable indicator for phase transitions.

Conclusions:

• The new order parameter M effectively describes critical behaviors around YLES.
• M's finite value at YLES makes it a promising candidate for quantitative experimental measurement.
• This research provides a new tool for detecting and understanding phase transitions near YLES.