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Emergent spin

Creutz, Michael
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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. -- Highlights: •The spin–statistics theorem is not required for particles on a lattice. •Spin emerges dynamically when spinless fermions have a relativistic continuum limit. •Graphene and staggered fermions are examples of this phenomenon. •The phenomenon is intimately tied to chiral symmetry and fermion doubling. •Anomaly cancellation is a crucial feature of any valid lattice fermion action.

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDSCHIRAL SYMMETRYDIRAC EQUATIONEXCITATIONFERMIONSGRAPHENELATTICE FIELD THEORYLIMITING VALUESQUANTUM MECHANICSRELATIVISTIC RANGESPINSTATISTICS

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Creutz, Michael. 2014-03-15. Emergent spin. https://doi.org/10.1016/j.aop.2013.12.002

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