UC Santa Barbara

We study two distinct systems along a similar theme. In one, we present new theoretical studies of the optical properties of the $J_2$-$\lambda$ model for the materieal FeSc$_2$S$_4$, which places it 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 compute 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. In the other, through a mixture of analytic and numerical techniques, we explore the optimal approximation by a free Majorana state to individual disorder realizations of the Sachdev-Ye-Kitaev model, along with a generalization of it. We elucidate the properties of the known time-reversal symmetry breaking phase in the generalized model, finding strong evidence of "spin glass" order. For the Sachdev-Ye-Kitaev model itself, our results are inconclusive but suggest a similar order may be present at $T = 0$.