Phase Space Fractons

Area of Science:

• Theoretical physics
• Condensed matter physics

Background:

• Fracton models offer a framework for studying systems with subdimensional particles.
• Conservation laws, such as dipole or higher multipole moments, are key to constructing these models.
• Generalizing conservation laws to phase space is a crucial step for a comprehensive classification.

Purpose of the Study:

• To generalize the concept of multipole moment conservation to phase space for classical fracton models.
• To classify all possible classical fracton models based on phase-space multipole conservation laws.
• To analyze the dynamics of a newly proposed self-dual model with specific moment conservation.

Main Methods:

• Generalization of multipole moment conservation to include position and momentum.
• Classification of classical fracton models based on these generalized conservation laws.
• Analysis of the dynamical behavior of a self-dual model using theoretical methods.

Main Results:

• A comprehensive classification of classical fracton models with phase-space multipole conservation is presented.
• A novel self-dual model conserving both dipole and quadrupole moments in position and momentum is identified.
• Quasiperiodic orbits were discovered in the phase space of this model, demonstrating a departure from ergodic behavior.

Conclusions:

• Phase-space multipole conservation provides a powerful framework for classifying fracton models.
• The identified self-dual model exhibits unique dynamical properties, including non-ergodic behavior.
• These findings contribute to a deeper understanding of exotic phases of matter and particle dynamics.