Phonon Dynamics in Extended Kitaev Models

Abstract

Quantum spin liquid is a state of matter in which magnetic frustration and strong quantum fluctuations prevent magnetic order down to the lowest temperatures. It exhibits exotic properties such as long-range entanglement, fractionalized excitations and topological order which are of interest from a theoretical perspective as well as applications in quantum computation. The Kitaev honeycomb model is a rare example of an exactly solvable system with a quantum spin liquid (QSL) ground state, where spins fractionalize into itinerant Majorana fermions and localized Z₂ fluxes. Remarkably, it was proposed that this model may be realized in certain materials composed of heavy transition metal ions from the 4d and 5d groups, where strong spin-orbit coupling plays a key role. Notable candidate materials include the ruthenium compound 𝛼-RuCl₃ and the iridates 𝛽-Li₂IrO₃ and H₃LiIr₂O₆. Despite growing interest and the identification of promising materials, direct experimental observation of a quantum spin liquid remains notoriously difficult. A key challenge lies in the very nature of QSLs: the absence of conventional magnetic order even at the lowest temperatures. Most candidate Kitaev materials inevitably host residual interactions beyond the pure Kitaev exchange, such as Heisenberg and off-diagonal couplings, which tend to stabilize magnetic order and obscure the spin liquid ground state. Nevertheless, these materials often lie close to a QSL regime, and this proximity can manifest in their excitation spectra. Dynamical probes, such as inelastic neutron scattering, Raman spectroscopy, and terahertz measurements have proven crucial in detecting signatures of fractionalized excitations characteristic of spin liquids. Even in magnetically ordered states, such experiments can reveal features of spin-liquid-like dynamics, offering a window into the underlying fractionalized physics. Furthermore, external tuning parameters such as magnetic field and pressure provide valuable tools for suppressing non-Kitaev interactions, destabilizing magnetic order, and pushing the system closer to the spin liquid phase. This tunability makes Kitaev materials an exciting platform for exploring quantum spin liquids and their unconventional excitations in realistic settings. Recently it was shown that phonon dynamics is an indirect but effective probe to study fractionalized excitations in the Kitaev spin liquid. In particular, ultrasound measurements of the sound attenuation reveal a characteristic temperature dependence which is in agreement with analytical calculations for the acoustic phonons coupled to the pure Kitaev spin liquid state. For a more comprehensive understanding of the signatures of fractionalization observed in experiments it is important to include non-Kitaev interactions and study the effects of magnetic field and pressure. This dissertation presents a mean-field study of phonon dynamics in the generalized J-K-𝛤 model, which is relevant for understanding experimental signatures in candidate Kitaev materials. Our analysis shows that as long as the system remains in the spin liquid phase, key features of the phonon response, linked to the presence of fractionalized excitations, persist even in the presence of residual interactions. Additionally, we provide a theoretical framework to interpret experimental observations under external tuning parameters such as magnetic field and pressure, which are commonly used to access or approach the spin liquid regime.