Signatures of Spinon Dynamics and Phase Structure of Dipolar-Octupolar Quantum Spin Ices in Two-Dimensional Coherent Spectroscopy.

We study how sharp signatures of fractionalization emerge in nonlinear spectroscopy experiments on spin liquids with separated energy scales. Our model is that of dipolar-octupolar rare earth pyrochlore materials, prime candidates for realizing quantum spin ice. This family of three-dimensional quantum spin liquids exhibits fractionalization of spin degrees of freedom into spinons charged under an emergent U(1) gauge field. We show that the technique of two-dimensional coherent spectroscopy can identify clear signatures of fractionalized spinon dynamics in dipolar-octupolar quantum spin ices. However, at intermediate temperatures, spinon dynamics are heavily constrained in the presence of an incoherent spin background, leading to a broad two-dimensional coherent spectroscopy response. At lower temperatures, a sharp signal emerges as the system enters a coherent spin liquid state. This lower temperature signal can in turn distinguish between zero-flux and π-flux forms of quantum spin ice.