Kibble-Zurek Scaling in the Yang-Lee Edge Singularity

Area of Science:

• Quantum physics
• Non-Hermitian systems
• Phase transitions

Background:

• Conventional phase transitions are typically studied in Hermitian systems and follow the Kibble-Zurek mechanism.
• Yang-Lee edge singularities (YLESs) represent critical points in non-Hermitian systems, exhibiting unique behaviors.
• Driven dynamics across critical points are crucial for understanding system responses to external perturbations.

Purpose of the Study:

• To investigate the driven dynamics across Yang-Lee edge singularities (YLESs) in a finite-size quantum Ising chain.
• To explore how system size and dimensionality affect the universal scaling behaviors of these dynamics.
• To compare the driven dynamics in YLESs with conventional phase transitions described by the Kibble-Zurek mechanism.

Main Methods:

• Utilizing a finite-size quantum Ising chain model with an imaginary symmetry-breaking field.
• Simulating driven dynamics across critical points by tuning dissipation strength.
• Analyzing the scaling behavior of the dynamics and comparing it with theoretical predictions.

Main Results:

• Phase transitions induced by dissipation in non-Hermitian systems can occur at finite size.
• For small system sizes, driven dynamics follow Kibble-Zurek scaling with (0+1)-dimensional YLES exponents.
• For medium system sizes, driven dynamics exhibit Kibble-Zurek scaling with exponents from both (0+1)-D and (1+1)-D YLESs.

Conclusions:

• The Kibble-Zurek mechanism can describe driven dynamics across YLESs, but the relevant critical exponents depend on system size and dimensionality.
• The breakdown of topological defect formation in YLESs does not preclude universal scaling behaviors.
• This study provides insights into the unique critical phenomena in non-Hermitian quantum systems.