Neural Quantum States of frustrated magnets: generalization and sign structure

TL;DR

This paper investigates the effectiveness of neural quantum states in modeling frustrated magnets, highlighting challenges in generalization and sign structure learning, which are crucial for realistic quantum system simulations.

Contribution

The study identifies the main factors affecting NQS applicability to frustrated magnets, emphasizing the importance of generalization over expressibility and analyzing sign structure learning difficulties.

Findings

Generalization quality drops with increased frustration.

Learning sign structure is more challenging than amplitudes.

Addressing generalization is key for realistic quantum simulations.

Abstract

Neural quantum states (NQS) attract a lot of attention due to their potential to serve as a very expressive variational ansatz for quantum many-body systems. Here we study the main factors governing the applicability of NQS to frustrated magnets by training neural networks to approximate ground states of several moderately-sized Hamiltonians using the corresponding wavefunction structure on a small subset of the Hilbert space basis as training dataset. We notice that generalization quality, i.e. the ability to learn from a limited number of samples and correctly approximate the target state on the rest of the space, drops abruptly when frustration is increased. We also show that learning the sign structure is considerably more difficult than learning amplitudes. Finally, we conclude that the main issue to be addressed at this stage, in order to use the method of NQS for simulating realistic models, is that of generalization rather than expressibility.