Symmetry Breaking and Lattice Kirigami

Area of Science:

• Quantum Field Theory
• Condensed Matter Physics
• Geometric Deformation

Background:

• Interacting quantum field theories on curved manifolds are crucial for understanding diverse physical phenomena.
• Geometric manipulation of lattices can introduce non-trivial curvature.
• Defects in materials can significantly alter local physical properties.

Purpose of the Study:

• To investigate the behavior of quantum fields on a curved 2D manifold constructed from a deformed hexagonal lattice.
• To explore the interplay between local curvature and boundary conditions in altering symmetry breaking.
• To analyze the impact of geometric defects on the order parameter of a quantum field theory.

Main Methods:

• Constructing a curved 2D manifold via geometric deformation of a hexagonal lattice with a defect.
• Imposing boundary conditions modulated by the geometry, assimilated by a nondynamical gauge field.
• Analyzing symmetry breaking and order parameter behavior in the presence of competing curvature and boundary effects.

Main Results:

• The geometric deformation results in locally nonvanishing curvature (positive or negative).
• Boundary conditions, modulated by geometry, act like a nondynamical gauge field.
• A competition between curvature and boundary conditions leads to surprising order parameter behavior near the defect.

Conclusions:

• The interplay of curvature and boundary conditions significantly impacts symmetry breaking in quantum field theories.
• The observed phenomenon is expected to be generic for such engineered geometries.
• This approach offers insights into systems with competing geometric and boundary influences.