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Title: Emergent spin

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.
Authors:
Publication Date:
OSTI Identifier:
22224296
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 342; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CHIRAL SYMMETRY; DIRAC EQUATION; EXCITATION; FERMIONS; GRAPHENE; LATTICE FIELD THEORY; LIMITING VALUES; QUANTUM MECHANICS; RELATIVISTIC RANGE; SPIN; STATISTICS