Emergent spin

Understand

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.