Daily Overview: This post sorts papers by relevance to nickelate superconductors. Summaries are AI-generated and may contain errors. arXiv submission processing window: times are unavailable (UTC).

1. Emergence of Kugel-Khomskii physics in quarter-filled bilayer correlated systems

Summary: This study investigates a quarter-hole-filled two-orbital bilayer Hubbard model inspired by transition metal bilayer systems. By explicitly treating the strong interlayer bonding of the dz2 orbital in a molecular orbital basis and projecting out high-energy electronic states, we derive a low-energy effective Kugel-Khomskii Hamiltonian that describes the coupling between electron spins and layer pseudospins. Combining Weiss mean-field theory with generalized flavor-wave theory, we reveal a rich ground-state phase diagram, including ferromagnetic and antiferromagnetic phases accompanied by layer-staggered charge-density order, a layer-coherent phase with spontaneous interlayer quantum coherence, and a novel maximal spin-layer entangled phase. This entangled phase arises from an emergent O(4) symmetry that is spontaneously broken to O(3), and its excitation spectrum features three gapless Goldstone modes that are entangled. The results suggest a geometry-driven mechanism for realizing composite entanglement in strongly correlated bilayer systems, and provide a concrete theoretical framework for understanding bilayer nickelate superconductors and other multi-component correlated materials.