Diffusion and relaxation of topological excitations in layered spin liquids

TL;DR

This paper investigates the dynamics of topological excitations in layered quantum spin liquids, revealing subdiffusive and logarithmic spreading behaviors, and proposes experimental signatures for detecting these excitations.

Contribution

It introduces exact solutions and simulations for diffusion equations in layered topological phases, highlighting unique signatures in pump-probe experiments and new decay laws.

Findings

Surface excitations spread subdiffusively with mean depth ~ t^{1/3}

Pair-annihilation causes logarithmic spreading of excitations

Total density decays as (log^2 t)/t, slower than in 2D systems

Abstract

Relaxation processes in topological phases such as quantum spin liquids are controlled by the dynamics and interaction of fractionalized excitations. In layered materials hosting two-dimensional topological phases, elementary quasiparticles can diffuse freely within the layer, whereas only pairs (or more) can hop between layers - a fundamental consequence of topological order. Using exact solutions of emergent nonlinear diffusion equations and particle-based stochastic simulations, we explore how pump-probe experiments can provide unique signatures of the presence of $2d$ topological excitations in a $3d$ material. Here we show that the characteristic time scale of such experiments is inversely proportional to the initial excitation density, set by the pump intensity. A uniform excitation density created on the surface of a sample spreads subdiffusively into the bulk with a mean depth $\bar z$ scaling as $\sim t^{1/3}$ when annihilation processes are absent. The propagation becomes logarithmic, $\bar z \sim \log t$, when pair-annihilation is allowed. Furthermore, pair-diffusion between layers leads to a new decay law for the total density, $n(t) \sim (\log^2 t)/t$ - slower than in a purely $2d$ system. We discuss possible experimental implications for pump-probe experiments in samples of finite width.