New Approach to Many-Body Ground State and Lowly Excited State Energies by Convolutional Neural Networks

Chen Yu Liu^1*, Daw Wei Wang¹

¹Department of Physics, National Tsing Hua University, Hsinchu, Taiwan

* Presenter:Chen Yu Liu, email:ef850502@gmail.com

The eigenvalue problem of a quantum many-body system is a challenging topic since the dimension of Hilbert space (and hence computational memory) grows exponentially as the system size increases. Here we propose a completely new method based on the pattern recognition of Convolutional Neuronal Networks, where the ground state and lowly excited state energies are extracted from a large random sampling of the many-body Hamiltonian. We use 1D Ising Model with a transverse field as an example, and show how the ground state degeneracy could be predicted and lifted near the quantum phase transition point, even though the model is trained by data in the perturbative regime.

Keywords: many-body system, neural network