Machine learning topological defeats formation with neural networks in a quantum phase transition

by Dr 石 汉清

Monday 18 Sep 2023, 00:00 → 02:00 Asia/Shanghai

318 (数理楼)

The strong representing power of neural networks make it become a powerful tool for solving quantum many-body systems. Except for static solutions, nonequilibrium processes are more challenging for neural networks. We study time evolutions of the energy spectra and the universal statistics of topological defects beyond Kibble-Zurek mechanism after a quantum phase transition in a transverse Ising model by virtue of the state-of-the-art neural networks and machine learning methods. This algorithm has two steps. First step is to represent the ground state of paramagnetic phase with neural network quantum state and machine learning; The second step is to quench the system from paramagnetic phase to ferromagnetic phase with time dependent variational Monte Carlo method. During the quantum phase transition, topological defeats will emerge due to Kibble-Zurek mechanism by neural network. The first three cumulants of the topological defect numbers and the energy spectra for this transverse Ising model are computed after a linear quench. The resulting outcomes match the analytical predictions very well.

 

arXiv: 2204.06769