Symmetries and many-body excited states with neural-network quantum states

TL;DR

This paper extends neural-network quantum states methods to efficiently find and analyze excited states in many-body quantum systems, including symmetry-targeted and non-symmetry states, demonstrating accuracy and architectural insights.

Contribution

It introduces new algorithms for targeting excited states with neural networks, including symmetry targeting and non-symmetry algorithms, validated on quantum models.

Findings

Deep networks outperform shallow ones for high-energy states.

Good agreement with exact results for excited states.

Effective methods for symmetry and non-symmetry excited states.

Abstract

Artificial neural networks have been recently introduced as a general ansatz to compactly represent many- body wave functions. In conjunction with Variational Monte Carlo, this ansatz has been applied to find Hamil- tonian ground states and their energies. Here we provide extensions of this method to study properties of ex- cited states, a central task in several many-body quantum calculations. First, we give a prescription that allows to target eigenstates of a (nonlocal) symmetry of the Hamiltonian. Second, we give an algorithm that allows to compute low-lying excited states without symmetries. We demonstrate our approach with both Restricted Boltzmann machines states and feedforward neural networks as variational wave-functions. Results are shown for the one-dimensional spin-1/2 Heisenberg model, and for the one-dimensional Bose-Hubbard model. When comparing to available exact results, we obtain good agreement for a large range of excited-states energies. Interestingly, we also find that deep networks typically outperform shallow architectures for high-energy states.