# Learning topological defects formation with neural networks in a quantum phase transition

arXiv: https://arxiv.org/abs/2204.06769 · HTML: https://mlsanity.com/paper/2204.06769/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 58 references that are in the map.
- First posted on arXiv 14 Apr 2022.

## Builds on (most cited first, 2 of 2)

- [Machine Learning in the Search for New Fundamental Physics](https://mlsanity.com/paper/2112.03769/) (2021)
- [Geometry of learning neural quantum states](https://mlsanity.com/paper/1910.11163/) (2019)

## Abstract (arXiv)

Neural networks possess formidable representational power, rendering them invaluable in solving complex quantum many-body systems. While they excel at analyzing static solutions, nonequilibrium processes, including critical dynamics during a quantum phase transition, pose a greater challenge for neural networks. To address this, we utilize neural networks and machine learning algorithms to investigate the time evolutions, universal statistics, and correlations of topological defects in a one-dimensional transverse-field quantum Ising model. Specifically, our analysis involves computing the energy of the system during a quantum phase transition following a linear quench of the transverse magnetic field strength. The excitation energies satisfy a power-law relation to the quench rate, indicating a proportional relationship between the excitation energy and the kink numbers. Moreover, we establish a universal power-law relationship between the first three cumulants of the kink numbers and the quench rate, indicating a binomial distribution of the kinks. Finally, the normalized kink-kink correlations are also investigated and it is found that the numerical values are consistent with the analytic formula.