Maxwell electromagnetism as an emergent phenomenon in condensed matter

Abstract

The formulation of a complete theory of classical electromagnetism by Maxwell is one of the milestones of science. The capacity of many-body systems to provide emergent mini-universes with vacua quite distinct from the one we inhabit was only recognised much later. Here, we provide an account of how simple systems of localised spins manage to emulate Maxwell electromagnetism in their low-energy behaviour. They are much less constrained by symmetry considerations than the relativistically invariant electromagnetic vacuum, as their substrate provides a non-relativistic background with even translational invariance broken. They can exhibit rich behaviour not encountered in conventional electromagnetism. This includes the existence of magnetic monopole excitations arising from fractionalisation of magnetic dipoles; as well as the capacity of disorder, by generating defects on the lattice scale, to produce novel physics, as exemplified by topological spin glassiness or random Coulomb magnetism.

Talk at Royal Society Symposium, "Unifying Physics and Technology in the Light of Maxwell's Equations", November 2015

References in corpus (6)

• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Dirac Strings and Magnetic Monopoles in Spin Ice Dy2Ti2O7
• Why spin ice obeys the ice rules
• Three dimensional resonating valence bond liquids and their excitations
• A Three Dimensional Kasteleyn Transition: Spin Ice in a [100] Field
• The Kasteleyn transition in three dimensions: spin ice in a [100] field

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• Emergent particles and gauge fields in quantum matter
• Structural magnetic glassiness in spin ice Dy${}_2$Ti${}_2$O${}_7$
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Square ice Coulomb phase as a percolated vertex lattice
• Unusual Coulomb phase physics in the arctic square ice