Navigating the Quantum Complexity of Matter

Marco Buongiorno Nardelli, University of North Texas, SFI

The space of possible materials is effectively infinite, and the rules governing it are quantum mechanical and therefore irreducible to simple intuition. Like a flock of birds whose collective behavior cannot be predicted from the rules of a single bird, electrons in a crystal follow local quantum rules that generate global emergent order superconductivity, topological protection, anomalous transport with no classical analogue. Discovering and engineering these states requires navigating a vast, high-dimensional landscape. I will describe a computational framework that makes this navigation tractable, built around a large materials database, an efficient quantum transport engine, and a parameter-free theory of strongly correlated electrons. The framework rests on compressing the full quantum state of a solid into the smallest faithful representation that still reproduces all relevant physics, then using that compressed form to compute topological invariants and transport coefficients efficiently enough to screen thousands of compounds. Pushed to systems with thousands of atoms, the same approach connects naturally to themes central to complexity science: the search for minimal sufficient descriptions, the navigation of high-dimensional fitness landscapes, and the stability of self-consistent solutions. The goal is a predictive map of the phase space of matter, at genomic scale.

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