Emergent spin

TL;DR

This paper explores how spin-statistics constraints emerge in lattice models that approximate relativistic quantum field theories, focusing on models like graphene where spin-less fermions exhibit relativistic behavior.

Contribution

It demonstrates how relativistic spin-statistics constraints can emerge from lattice models with spin-less fermions, connecting lattice systems to continuum relativistic theories.

Findings

Lattice models can produce relativistic fermionic excitations

Graphene exemplifies emergent relativistic behavior

Spin-statistics constraints emerge in continuum limit

Abstract

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.