Deep Learning-Based Method for a Ground-State Solution of Bose-Fermi Mixture at Zero Temperature

A Bose-Fermi mixture, consisting of both bosons and fermions, exhibits distinctive quantum coherence and phase transitions, offering valuable insights into many-body quantum systems. The ground state, as the system’s lowest energy configuration, is essential for understanding its overall behavior. In this study, we introduce the Bose-Fermi Energy-based Deep Neural Network (BF-EnDNN), a novel deep learning approach designed to solve the ground-state problem of Bose-Fermi mixtures at zero temperature through energy minimization. This method incorporates three key innovations: point sampling pre-training, a Dynamic Symmetry Layer (DSL), and a Positivity Preserving Layer (PPL). These features significantly improve the network’s accuracy and stability in quantum calculations. Our numerical results show that BF-EnDNN achieves accuracy comparable to traditional finite difference methods, with effective extension to two-dimensional systems. The method demonstrates high precision across various parameters, making it a promising tool for investigating complex quantum systems.