Model-Independent Sum Rule Analysis Based on Limited-Range Spectral Data

Abstract

Partial sum rules are widely used in physics to separate low- and high-energy degrees of freedom of complex dynamical systems. Their application, though, is challenged in practice by the always finite spectrometer bandwidth and is often performed using risky model-dependent extrapolations. We show that, given spectra of the real and imaginary parts of any causal frequency-dependent response function (for example, optical conductivity, magnetic susceptibility, acoustical impedance etc.) in a limited range, the sum-rule integral from zero to a certain cutoff frequency inside this range can be safely derived using only the Kramers-Kronig dispersion relations without any extra model assumptions. This implies that experimental techniques providing both active and reactive response components independently, such as spectroscopic ellipsometry in optics, allow an extrapolation-independent determination of spectral weight 'hidden' below the lowest accessible frequency.

5 pages, 3 figures

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• Impact of a finite cut-off for the optical sum rule in the superconducting state
• Mott transition and collective charge pinning in electron doped Sr2IrO4
• Signatures of three-dimensional photo-induced superconductivity in YBa${}_2$Cu${}_3$O${}_{6.48}$
• The fate of quasiparticles in the superconducting state