Symmetry Breaking and Lattice Kirigami

Abstract

In this work we consider an interacting quantum field theory on a curved two-dimensional manifold that we construct by geometrically deforming a flat hexagonal lattice by the insertion of a defect. Depending on how the deformation is done, the resulting geometry acquires a locally non-vanishing curvature that can be either positive or negative. Fields propagating on this background are forced to satisfy boundary conditions modulated by the geometry and that can be assimilated by a non-dynamical gauge field. We present an explicit example where curvature and boundary conditions compete in altering the way symmetry breaking takes place, resulting in a surprising behaviour of the order parameter in the vicinity of the defect. The effect described here is expected to be generic and of relevance in a variety of situations.

6 pages; 2 figures

References in corpus (15)

• The electronic properties of graphene
• Atomic-scale control of graphene magnetism using hydrogen atoms
• Interactions and phase transitions on graphene's honeycomb lattice
• How close can one approach the Dirac point in graphene experimentally?
• Thermal Hall Effect and Geometry with Torsion
• Interacting fermions in rotation: chiral symmetry restoration, moment of inertia and thermodynamics
• Density-curvature response and gravitational anomaly
• Boundary effects and gapped dispersion in rotating fermionic matter
• Anomalous effects of dense matter under rotation
• Edge states and thermodynamics of rotating relativistic fermions under magnetic field
• Chiral gap effect in curved space
• A cosmological model for corrugated graphene sheets
• Lattice QCD in curved spacetimes
• Geometrically induced magnetic catalysis and critical dimensions
• Lattice gauge theory and gluon color-confinement in curved spacetime

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• Probing non-Hermitian phase transitions in curved space via quench dynamics
• Symmetry breaking and lattice kirigami: finite temperature effects
• Landau levels in curved space realized in strained graphene
• $(\mathcal{F},\mathcal{G})$-summed form of the QED effective action
• Finite temperature fermionic condensate in a conical space with a circular boundary and magnetic flux
• R-summed form of adiabatic expansions in curved spacetime
• Reduced quantum electrodynamics in curved space
• The Casimir effect for nonlinear sigma models and the Mermin-Wagner-Hohenberg-Coleman theorem
• Tunable Dirac points and zero-energy modes in periodic curved graphene superlattices
• Gauge fields induced by curved spacetime
• Spontaneously broken symmetry restoration of quantum fields in the vicinity of neutral and electrically charged black holes
• Tunable Topological Phases in Quantum Kirigamis