Disorder-Induced Anomalous Diffusion in a 3D Spin Network

Abstract

Emergent hydrodynamics (EHD) bridges short-time unitarity with late-time thermodynamics, universal transport phenomena characterize the manner and speed of transport and thermalization. Typical non-integrable systems with few conserved local quantities are expected to be diffusive. In contrast, strongly disordered systems which admit phases such as many-body localization, are predicted to inhibit thermalization and thus slow dynamical transport. Disordered systems represent a uniquely poised platform to probe the quantum-to-classical transition and the emergence of irreversible thermodynamics from the underlying unitary structure. Here, we study a strongly disordered nuclear spin ensemble, using local measurements enabled by the disordered-state technique. We observe an apparent phase transition into a sub-diffusive regime, which we model as a random walk on the emergent fractal structure of a percolating network in the dipolar spin ensemble. Our novel theoretical model provides a framework for characterizing the emergence of thermalization in closed quantum systems, even in the presence of strong disorder.

Figures (1)

• Figure 1: Here we show some of the details of the experimental system, and the collected hydrodynamic data. In panel (a), graphically depict the lithium (red) fluoride (blue) crystal structure. Each lithium spin is contributing to the disordered field of many fluorine spins, leading to spatial correlations with a $1/r^3$ profile. In panel (b), we provide a graphical depiction of our experimental sequencing -- a carefully engineered unitary transport block sandwiched by disordered state and observable blocks. Below the crystal structure, in panel (c), is an illustrative cartoon of the two conjectured hydrodynamic phases -- fully all-to-all connected in the weak disorder limit, and very sparsely connected in the strong disorder (fractal) limit. Due to the limited connectivity, large detours serve as deep traps and slow transport into a sub-diffusive phase. In panel (d) we plot two illustrative time-traces: one diffusive and one sub-diffusive. Finally, in panel (e), we plot the fitted survival probability exponent, $\gamma$, as a function of the quenched disorder strength generated by the Lithium spins, in units of $J_{nn}$.