Using Matrix Product States to Study the Dynamical Large Deviations of Kinetically Constrained Models.

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Computational Physics

Background:

• Kinetically constrained models (KCMs) are crucial for understanding glass dynamics.
• Analyzing rare event statistics in KCMs is computationally challenging.
• Existing methods limit the study of system sizes and finite-size effects.

Purpose of the Study:

• To demonstrate the applicability of tensor network techniques for rare event statistics in KCMs.
• To enable the study of larger system sizes and more detailed finite-size scaling.
• To investigate the spectral gaps and dynamical phase properties of KCMs.

Main Methods:

• Application of tensor network techniques, specifically variational matrix product states.
• Numerical approximation of leading eigenstates of tilted dynamical generators.
• Analysis of Fredrickson-Andersen and East models as paradigmatic KCM examples.

Main Results:

• Tensor networks provide systematic and high-accuracy approximations for rare event statistics.
• The method allows for the study of system sizes beyond the reach of other techniques.
• Detailed characterization of finite-size scaling, spectral gaps, and dynamical phase properties was achieved.

Conclusions:

• Tensor network techniques are powerful tools for studying KCMs and rare event statistics.
• This approach opens new avenues for understanding complex dynamics in disordered systems.
• The findings have broader implications for statistical mechanics and computational physics.