Generalized dynamic scaling for quantum critical relaxation in imaginary time.

Area of Science:

• Quantum physics
• Condensed matter theory
• Statistical mechanics

Background:

• Studying quantum critical dynamics is crucial for understanding phase transitions.
• Previous models for initial order parameter behavior under scale transformations were limited.
• Quantum systems exhibit unique relaxation behaviors near critical points.

Purpose of the Study:

• To investigate imaginary-time relaxation critical dynamics in quantum systems.
• To develop a universal description for the initial order parameter's behavior.
• To establish a characteristic function applicable to quantum critical dynamics.

Main Methods:

• Analysis of imaginary-time relaxation dynamics.
• Theoretical development of a universal characteristic function.
• Numerical simulations using the one-dimensional transverse-field Ising model.
• Verification of universality across different models in the same universality class.

Main Results:

• The initial order parameter's behavior deviates from simple power laws under scale transformations.
• A universal characteristic function accurately describes rescaled initial magnetization.
• This function is valid for both short- and long-time dynamics near the quantum critical point.
• Numerical simulations confirm the function's applicability and universality.

Conclusions:

• A universal characteristic function provides a robust framework for quantum critical dynamics.
• The findings extend concepts from classical critical dynamics to the quantum realm.
• The study offers a new tool for analyzing and predicting quantum system behavior near criticality.