Theory of excitations and dielectric response at a spin-orbital quantum critical point

TL;DR

This paper develops a theoretical framework for understanding the excitations and dielectric response at a quantum critical point in a spin-orbital system, providing insights into the collective excitations near quantum phase transitions.

Contribution

It introduces a detailed analysis of optical properties and quasiparticle excitations in the $J_2$-$mbda$ model near a quantum critical point, linking theory with experimental observations.

Findings

Dispersion relation for quasiparticles computed

Collective response to electric field characterized

Results support the $J_2$-$mbda$ model's relevance

Abstract

Despite possessing a local spin $2$ moment on the iron site and a Curie-Weiss temperature of $45K$, the A site spinel FeSc$_2$S$_4$ does not magnetically order down to 50mK. Previous theoretical work by Chen and Balents advanced an explanation for this observation in the form of the "$J_2$-$\lambda$" model which places FeSc$_2$S$_4$ close to a quantum critical point on the disordered side of a quantum phase transition between a N\'{e}el ordered phase and a "Spin-Orbital Liquid" in which spins and orbitals are entangled, quenching the magnetization. We present new theoretical studies of the optical properties of the $J_2$-$\lambda$ model, including a computation of the dispersion relation for the quasiparticle excitations and the form of the collective response to electric field. We argue that the latter directly probes a low energy excitation continuum characteristic of quantum criticality, and that our results reinforce the consistency of this model with experiment.