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Title: Measure the emergent-photon $T^3$ heat capacity and speed in quantum spin ice
Plain: Emergent photons should add a heat capacity growing as the cube of temperature, like lattice vibrations, with a size fixed by the photon speed. Measuring it and matching the speed predicted from the measured interactions would be a sharp test.
Precise: In quantum spin ice the photon speed $c$ is set by the ring-exchange scale $g=12J_{\mathrm{pm}}^{3}/J_{\mathrm{zz}}^{2}$ (c ~ g $a$/hbar up to a computed prefactor, a the lattice spacing), and the photon heat capacity per volume is C/V = (4 pi^2/15) k_B (k_B T/hbar c)^3 for two polarizations. Measure $C/T^{3}$ below the photon bandwidth in a candidate material and compare $c$ with the value from independently fitted exchange parameters. An answer is $c$ measured and predicted, with agreement or disagreement within errors.
Settled by: Heat capacity below about 0.05 K with nuclear and phonon contributions subtracted, compared with the photon speed from neutron spectra and quantum Monte Carlo.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
Status note: (empty)
Posed since: (empty)