Design principles of deep translationally-symmetric neural quantum states for frustrated magnets

TL;DR

This paper explores the design of deep neural network architectures, specifically ConvNext, for accurately modeling ground states of frustrated quantum magnets, revealing insights into their effectiveness and proposing optimized network configurations.

Contribution

It introduces the application of ConvNext architecture to quantum many-body ground states and provides a blueprint for designing translationally-symmetric neural networks for frustrated magnetism.

Findings

ConvNext performs well with low computational cost.

Achieves competitive variational energies on frustrated spin models.

Relates ConvNext to transformer-based architectures for quantum states.

Abstract

Deep neural network quantum states have emerged as a leading method for studying the ground states of quantum magnets. Successful architectures exploit translational symmetry, but the root of their effectiveness and differences between architectures remain unclear. Here, we apply the ConvNext architecture, designed to incorporate elements of transformers into convolutional networks, to quantum many-body ground states. We find that it is remarkably similar to the factored vision transformer, which has been employed successfully for several frustrated spin systems, allowing us to relate this architecture to more conventional convolutional networks. Through a series of numerical experiments we design the ConvNext to achieve greatest performance at lowest computational cost, then apply this network to the Shastry-Sutherland and J1-J2 models, obtaining variational energies comparable to the state of the art, providing a blueprint for network design choices of translationally-symmetric architectures to tackle challenging ground-state problems in frustrated magnetism.