The kagome lattice, with its unique geometric structure, has emerged as a leading platform for exploring quantum many-body physics, particularly in the study of quantum spin liquids (QSLs) and unconventional superconductivity. This review highlights recent advancements in the investigations of QSLs, fractional magnetization plateau phases in kagome antiferromagnets, and unconventional superconductivity in vanadium-based kagome superconductors. We begin by examining the classical ground-state properties of the nearest-neighbor kagome antiferromagnetic Heisenberg model and introducing recent experimental progress in the study of QSLs and fractional magnetization plateau phases. Next, we discuss the fermionic description of the QSL states, along with related gauge theory and the variational Monte Carlo (VMC) method. We then focus on discussing the VMC studies of QSLs and magnetization plateau phases in kagome antiferromagnets. For superconductivity in kagome systems, we first analyze the characteristics of the electronic structure and the possible associated electronic instabilities. Finally, we review recent experimental advances in unconventional superconductivity in AV₃Sb₅ (A = K, Rb, Cs), with a particular focus on chiral superconductivity and pairing density waves.
He et al. (2025) studied this question.