Abstract
Strongly correlated electrons have long been a central subject of condensed matter physics. In this thesis, we approach them through localization: electrons localized in two-dimensional crystals underpin the two themes developed here. First, localization makes quantum states constructible.
When a free-fermion ground state is spanned by exponentially localized Wannier functions, its tensor-network representation can be constructed directly. We present a stackedtree algorithm that builds projected entangled pair states for such systems without variational optimization, and demonstrate it on obstructed atomic insulators in one and two dimensions. Second, localization is a route to strong correlation, because quenching the kinetic energy makes the interaction effectively strong. The kagome lattice reaches this limit by geometry. Destructive interference confines electrons to single hexagons, and the band spanned by these localized states is flat, so the interactions can no longer be neglected. In collaboration with scanning tunneling microscopy experiments on Fe-doped CoSn, we identify the inter-band nematic order parameter and the orbital-selective Mott state realized in its partially filled flat bands. We further map the competition among ferromagnetism, nematicity, and Fermi-surface-nesting-driven orders using self-consistent Hartree–Fock theory, and find nematicity to be the dominant phase across a wide range of fillings, consistent with the experimental observations.