Hybrid convolutional neural network and PEPS wave functions for quantum many-particle states

TL;DR

This paper introduces a hybrid wave function combining CNN and PEPS for quantum many-particle states, effectively capturing sign structures and amplitudes, leading to competitive ground state energies in frustrated spin models.

Contribution

It presents a novel hybrid ansatz that integrates PEPS for sign structure and CNN for amplitudes, improving variational wave function accuracy.

Findings

Achieves ground energies competitive with state-of-the-art methods.

Demonstrates effectiveness on the frustrated spin-1/2 J1-J2 model.

Shows the hybrid approach captures complex quantum correlations.

Abstract

Neural networks have been used as variational wave functions for quantum many-particle problems. It has been shown that the correct sign structure is crucial to obtain the high accurate ground state energies. In this work, we propose a hybrid wave function combining the convolutional neural network (CNN) and projected entangled pair states (PEPS), in which the sign structures are determined by the PEPS, and the amplitudes of the wave functions are provided by CNN. We benchmark the ansatz on the highly frustrated spin-1/2 $J_1$-$J_2$ model. We show that the achieved ground energies are competitive to state-of-the-art results.