Solving the nuclear pairing model with neural network quantum states

Abstract

We present a variational Monte Carlo method that solves the nuclear many-body problem in the occupation number formalism exploiting an artificial neural network representation of the groundstate wave function. A memory-efficient version of the stochastic reconfiguration algorithm is developed to train the network by minimizing the expectation value of the Hamiltonian. We benchmark this approach against widely used nuclear many-body methods by solving a model used to describe pairing in nuclei for different types of interaction and different values of the interaction strength. Despite its polynomial computational cost, our method outperforms coupled-cluster and provides energies that are in excellent agreement with the numerically-exact full configuration interaction values.

Lee-Yang theory of quantum phase transitions with neural network quantum states

“…Neural network quantum states are a recently developed class of variational states [8] that have shown great potential for parametrizing and finding the ground state of interacting quantum many-body systems [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Neural network quantum states represent the wave function of a quantum many-body system as a neural network.…”

“…They have already been applied to find the wave functions of several spin models [9][10][11][12][13][14]28], including the J 1 − J 2 Heisenberg model [15][16][17][18][19][20][21]. Moreover, their use has been extended to fermionic [22,29] and bosonic [30][31][32] systems, as well as to molecules [22,23] and nuclei [24][25][26].…”