Spinon walk in quantum spin ice

Spin ice is a frustrated magnet that displays rich emergent phenomena. For example, the magnetic moments carried by the spins may separate into mobile magnetic charges, giving rise to a novel fractional excitation known as the monopole. In the classical spin ice, the monopoles diffuse by virtue of thermal fluctuations. Their diffusion produces the unique dynamic properties of the classical spin ice. Quantum spin ice is a novel family of spin ice magnets that possess substantial quantum fluctuations. The fractional excitations are spinons, which are quantum analog of the monopoles in classical spin ice. As opposed to a diffusing monopole, the spinon propagates via quantum tunneling. Yet, different from a conventional quantum particle, the spinon moves in a background of disordered spins. The orientation of background spins controls the spinon motion, whereas the spinon motion in turn alters the spin background. We may ask whether there is a suitable framework for understanding the dynamics of spinon in quantum spin ice, and furthermore, whether the spinon propagation is coherent. In this talk, I will present our recent study on a minimal model that captures the essential features of single spinon dynamics in quantum spin ice. I will demonstrate that the spinon motion can be thought of as a quantum walk with entropy-induced memory. Our numerical simulation shows that the simple quasi-particle behavior emerges out of the intricate interplay between the spinon and the background spins.