Learning topological defects formation with neural networks in a quantum phase transition
This work addresses the problem of modeling critical dynamics in quantum systems for physicists, but it is incremental as it applies existing neural network methods to a specific quantum model.
The researchers tackled the challenge of analyzing nonequilibrium processes in a quantum phase transition by using neural networks to study topological defects in a one-dimensional transverse-field quantum Ising model, finding power-law relationships between excitation energy and kink numbers, and confirming a binomial distribution of kinks with correlations matching analytic predictions.
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.