Impact of Random Bond Disorder on Quantum Skyrmions in a spin-half Quantum Heisenberg Model

TL;DR

This study addresses how quenched random bond disorder affects quantum skyrmions in a spin-½ Heisenberg model with Dzyaloshinskii–Moriya interaction and anisotropy, using neural network quantum states to access large, disordered systems. The authors quantify spin textures, topological indices, and entanglement (via the second Rényi entropy and Kitaev–Preskill topological entanglement entropy) under Gaussian-distributed bond disorder with strength $\delta$, averaged over multiple realizations. They find that disorder destabilizes and ultimately collapses skyrmions around $\delta \approx 0.7$, while locally increasing entanglement (higher $S_2$) but leaving long-range entanglement negligible (nearly zero $S_{topo}$) across all disorder strengths. The results reveal a nuanced role for disorder: it degrades topological textures yet can enhance local quantum correlations, and they demonstrate limitations of $S_{topo}$ based on Rényi-2 entropy as a detector of skyrmion phases on square lattices. This work informs design principles for disorder-tolerant quantum skyrmion materials and showcases the capabilities and limits of neural-network quantum states in studying disordered topological textures.

Abstract

We investigate the impact of random bond disorder on quantum skyrmions using a spin-half quantum Heisenberg model on the square lattice with Dzyaloshinskii-Moriya interaction, Heisenberg anisotropy, and boundary-pinned magnetic field. Utilizing the neural network quantum state technique, we explore the influence of disorder on spin textures, topological properties, and quantum entanglement. We show that the disorder reduces the stability of quantum skyrmions, ultimately causing them to collapse at high disorder strengths. In addition, our results reveal two key insights. First, the presence of disorder, rather than simply degrading skyrmion order, significantly enhances local quantum entanglement, as evidenced by the rise in second Rényi entropy. Second, our calculations show that the topological entanglement entropy calculated using the second Rényi entropy remains negligible across all the disorder strengths. This suggests long-range entanglement is absent and the skyrmion phase is not detectable using this specific probe. Overall, our work provides new insights into how disorder constructively influences quantum materials.

Figures (12)

• Figure 1: Architecture of the NQS. The input is a lattice spin configuration in the $\sigma^z$ basis. Two separate neural networks are used to model the modulus $\rho$ and phase $\phi$ with each layer consists of $2L^2$ neurons. The output is the logarithm of the wave function.
• Figure 2: Spin configurations for $L = 7$ (a--c) and $L = 9$ (d--f) at different disorder strengths $\delta$ for $D = 0.8$ and $A = 0.3$, with color indicating local Rényi-2 entropy, and arrow length indicates the magnitude of the spin expectation value. Panels show (a,d) $\delta = 0.0$; (b,e) $\delta = 0.5$; and (c,f) $\delta = 1.5$.
• Figure 3: (a) Average spin magnitude, (b) Maximum spin magnitude, (c) Minimum spin magnitude, and (d) Spin magnitude range as a function of disorder strength for $L = 7$ and $L = 9$, with standard error bars over 50 disorder realizations.
• Figure 4: Disorder-averaged skyrmion number $C$ and skyrmion stability $Q$ as a function of disorder strength for (a) $L = 7$ and (b) $L = 9$, at fixed $D = 0.8$ and $A = 0.3$.
• Figure 5: Maximum Rényi-2 entropy as a function of disorder strength for $L = 7$ and $L = 9$ with standard error over 50 disorder realizations represented as bars.