The Flumen of Spectral Form: Emergent Geometry in Non-Fermi Liquids
The strange metal phase in high-temperature superconductors and heavy-fermion compounds has long resisted explanation within Landau's Fermi liquid framework. The spectral function—the single-particle excitation spectrum measured by photoemission—shows a broad, incoherent continuum with no sharp quasiparticle peak, and its temperature and frequency scaling follows power laws that defy the standard ω 2 + T 2 form. Over the past decade, a radical idea has gained traction: that this anomalous spectral shape is a signature of emergent geometry—a hidden curved spacetime in the low-energy theory. The flumen of spectral form, the flow of spectral weight across energy and momentum, may encode the curvature of an internal anti-de Sitter (AdS) space or the fractal geometry of a Sachdev-Ye-Kitaev (SYK) model.