Design principles of deep translationally-symmetric neural quantum states for frustrated magnets
arXiv:2505.03466 · doi:10.1103/ybgv-35jm
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.
15 pages, 8 figures, updated version
References in corpus (25)
- The density-matrix renormalization group in the age of matrix product states
- Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
- Quantum Spin Liquid in Spin 1/2 J1-J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections
- Transformer variational wave functions for frustrated quantum spin systems
- Gapless spin liquid and valence-bond solid in the Heisenberg model on the square lattice: insights from singlet and triplet excitations
- Empowering deep neural quantum states through efficient optimization
- Quantum-number projection in the path-integral renormalization group method
- High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks
- A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States
- Optimizing Design Choices for Neural Quantum States
- Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution
- Variational Monte Carlo with Large Patched Transformers
- Mapping of attention mechanisms to a generalized Potts model
- Investigating Topological Order using Recurrent Neural Networks
- Transformer Wave Function for two dimensional frustrated magnets: emergence of a Spin-Liquid Phase in the Shastry-Sutherland Model
- A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions
- Highly resolved spectral functions of two-dimensional systems with neural quantum states
- Neural Projected Quantum Dynamics: a systematic study
- Spin-1/2 kagome Heisenberg antiferromagnet: Machine learning discovery of the spinon pair density wave ground state
- Comment on "Can Neural Quantum States Learn Volume-Law Ground States?"
- Fine-tuning Neural Network Quantum States
- Are queries and keys always relevant? A case study on Transformer wave functions
- Accurate neural quantum states for interacting lattice bosons
- Approximately-symmetric neural networks for quantum spin liquids
- Efficiency of neural quantum states in light of the quantum geometric tensor