Executive Summary : | Quantum spin liquids (QSLs) are distinct states of matter that cannot be described by conventional order parameters. Honeycomb lattice quantum antiferromagnets (HQAFs) can stabilize a QSL state through anisotropic Kitaev magnetic interactions or magnetic frustration due to extended-range spin interactions. The most recently synthesized rare-earth HQAF, YbCl₃, is isostructural to the proximate Kitaev magnet α-RuCl₃ and was claimed to bear anisotropic magnetic interactions despite a Neel antiferromagetic ground state. However, a clear understanding of the crystal field effects on the magnon spectrum and the possibility of QSL states in rare-earth HQAF, RCl₃, is lacking. This study aims to investigate magnetic excitations and possible QSL phase(s) in HQAF using a self-consistent spin fluctuation approach from weak- to strong-coupling limits. The study will obtain the magnon spectrum, full spectral function, and quantum correction to magnetization. Crystal field effects in honeycomb RCl₃ will be obtained via density functional theory (DFT) calculations and incorporated in the spin-fluctuation approach. The study will also investigate possible quantum phase transitions, particularly the presence of a QSL state, via the renormalization of the AF gap and energy dispersion due to fermion-magnon interactions. |