Critical Relaxation in the Quantum Yang-Lee Edge Singularity.

Area of Science:

• Condensed matter physics
• Quantum magnetism
• Critical phenomena

Background:

• The quantum Ising chain is a fundamental model in condensed matter physics.
• Yang-Lee edge singularities (YLESs) represent critical points in statistical mechanics and quantum field theory.
• Understanding relaxation dynamics near critical points is crucial for characterizing system behavior.

Purpose of the Study:

• To investigate the relaxation dynamics of a quantum Ising chain in an imaginary longitudinal field.
• To identify and characterize scaling behaviors near Yang-Lee edge singularities (YLESs).
• To develop a theoretical framework describing these scaling properties.

Main Methods:

• Utilizing a polarized initial state in the quantum Ising chain.
• Analyzing the system's response under different Hamiltonians (paramagnetic, ferromagnetic, critical).
• Developing a scaling theory based on (0+1)-dimensional YLES.

Main Results:

• Observed manifestation of scaling behaviors in magnetization after a non-universal transient time.
• Paramagnetic Hamiltonian: periodic magnetization oscillations inversely proportional to the energy gap.
• Ferromagnetic Hamiltonian: magnetization decays to a saturated value.
• Critical Hamiltonian: linear increase in magnetization.
• The (0+1)-dimensional YLES effectively describes scaling behavior in small- to medium-sized systems.

Conclusions:

• The study reveals distinct relaxation dynamics near YLES in the quantum Ising chain.
• A developed scaling theory successfully describes these dynamics, particularly the role of (0+1)-dimensional YLES.
• These findings offer insights into critical phenomena and quantum system relaxation.