The Amplitude Mode in Condensed Matter : Higgs Hunting on a Budget

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The amplitude mode is a ubiquitous phenomenon in systems with broken continuous symmetry and effective relativistic dynamics, and has been observed in magnets, charge density waves, cold atom systems, and superconductors. It is a simple analog of the Higgs boson of particle physics. I will discuss the properties of the amplitude mode and its somewhat surprising visibility in two-dimensional systems, recently confirmed in cold atom experiments. The behavior in the vicinity of a quantum critical point will be stressed, comparing theoretical, numerical, and experimental results.