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

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, and then apply this network to the Shastry-Sutherland and <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>J</a:mi> <a:mn>1</a:mn> </a:msub> <a:mo>−</a:mo> <a:msub> <a:mi>J</a:mi> <a:mn>2</a:mn> </a:msub> </a:mrow> </a:math> 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.