Neural Quantum State in Matrix Quantum Mechanics

Matrix quantum mechanics are a class of models with emergent spatial dimensions. As quantum mechanical theories, they provide a clean framework for understanding microscopic aspects of holography. However, as interacting many-body systems, exact solutions are often unavailable. Starting with reviewing previously solved cases, we use variational quantum Monte Carlo with neural network ansatz for solving low-energy states in both bosonic and supersymmetric theories. The emergent locality is captured by an entanglement measure that we propose, and we comment on potential broader applications to holography.