Symmetry Breaking and Lattice Kirigami

TL;DR

This paper explores how geometric defects in a curved lattice influence symmetry breaking in quantum field theories, revealing complex interactions between curvature, boundary conditions, and order parameters.

Contribution

It introduces a model of quantum fields on a curved lattice with defects, demonstrating how geometry affects symmetry breaking and order parameters in novel ways.

Findings

Curvature and boundary conditions compete to alter symmetry breaking.

Order parameter behavior is significantly affected near defects.

The effects are expected to be generic across similar systems.

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.