Emergent spin Original Research Article

Quantum mechanics and relativity in the continuum imply the well known spin–statistics connection. However for particles hopping on a lattice, there is no such constraint. If a lattice model yields a relativistic field theory in a continuum limit, this constraint must “emerge” for physical excitations. We discuss a few models where a spin-less fermion hopping on a lattice gives excitations which satisfy the continuum Dirac equation. This includes such well known systems such as graphene and staggered fermions.