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

TL;DR

This paper develops a low-energy Kugel-Khomskii model for quarter-filled bilayer systems, revealing complex spin and charge phases, including a novel entangled phase with unique excitations, relevant to correlated materials like nickelates.

Contribution

It introduces a new effective Kugel-Khomskii Hamiltonian for bilayer systems with strong interlayer hybridization, uncovering exotic phases and entanglement mechanisms.

Findings

Discovery of a hidden spin-layer entangled phase.

Identification of a spontaneous interlayer quantum coherence.

Characterization of a unique Goldstone mode spectrum.

Abstract

We present a theoretical study of the low-energy physics of a quarter-hole-filled two-orbital bilayer Hubbard model motivated by transition-metal bilayer systems with strong orbital-selective interlayer hybridization. By explicitly treating the strong interlayer bonding of dz2 orbitals within a molecular orbital basis and projecting out high-energy electronic states, we derive a low-energy effective Kugel-Khomskii Hamiltonian describing the interplay between electron spin and emergent layer pseudospin degrees of freedom. We map out a rich ground state phase diagram featuring diverse spin and charge ordered states. These include conventional ferromagnetic and antiferromagnetic phases with layer staggered charge densities, a layer-coherent phase characterized by spontaneous interlayer quantum coherence, and a novel maximally spin-layer-entangled phase with a hidden composite spin-layer order. We show that this exotic hidden ordered phase arises from the spontaneous breaking of an emergent O(4) symmetry down to a O(3), manifesting a unique excitation spectrum with three entangled gapless Goldstone modes. Our results uncover a geometrically driven mechanism for realizing composite entanglement in strongly correlated bilayer systems and provide a concrete theoretical framework relevant to bilayer nickelate superconductors and other multi-component correlated materials.