Classical topological order in Abelian and non-Abelian generalized height models

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Lattice Models

Background:

• Exploring novel lattice models is crucial for understanding complex physical phenomena.
• Symmetry groups play a fundamental role in characterizing particle physics and condensed matter systems.
• Topological order and quasi-long-range order are key concepts in modern physics.

Purpose of the Study:

• To introduce and investigate a new class of lattice models based on finite symmetry groups.
• To explore the emergence of topological order from local constraints within these models.
• To characterize the ordering properties using Monte Carlo simulations.

Main Methods:

• Utilizing Monte Carlo simulations to study lattice models.
• Defining degrees of freedom as elements of finite Abelian or non-Abelian symmetry groups on directed edges.
• Implementing constraints where the plaquette group product equals the group identity.
• Analyzing topological sectors labeled by group products along nontrivial loops.

Main Results:

• Demonstrated that local non-Abelian constraints can lead to global topological liquid properties.
• Identified topological sectors labeled by group products along topologically nontrivial loops.
• Measured relative sector probabilities and defect pair distances to characterize order.

Conclusions:

• The studied lattice models exhibit unique topological properties arising from local symmetry constraints.
• These models provide a framework for understanding topological order in systems with finite symmetry groups.
• The findings suggest potential pathways to realizing topological states of matter.