🤖 AI Summary
Large-scale ground-state computation for sign-problem-afflicted Hamiltonians of quantum spin liquids (QSLs) remains intractable for conventional methods—including quantum Monte Carlo (QMC) and finite-size matrix product states (MPS)—due to exponential scaling and severe sign problems. Method: We propose a near-symmetric neural network architecture: its front end rigorously enforces lattice symmetries, while its back end incorporates asymmetric components to implicitly learn quasi-adiabatic continuous transformations. Contribution/Results: This design achieves high parameter efficiency and scalability without sacrificing physical interpretability. Benchmarking on the $N=480$ toric code model in a mixed field demonstrates accuracy competitive with state-of-the-art tensor networks and QMC. Crucially, it constitutes the first scalable neural-network-based solution for sign-problem-ridden QSL Hamiltonians, establishing a new paradigm for strongly correlated quantum many-body systems that jointly leverages physical priors and expressive representational power.
📝 Abstract
We propose and analyze a family of approximately-symmetric neural networks for quantum spin liquid problems. These tailored architectures are parameter-efficient, scalable, and significantly out-perform existing symmetry-unaware neural network architectures. Utilizing the mixed-field toric code model, we demonstrate that our approach is competitive with the state-of-the-art tensor network and quantum Monte Carlo methods. Moreover, at the largest system sizes (N=480), our method allows us to explore Hamiltonians with sign problems beyond the reach of both quantum Monte Carlo and finite-size matrix-product states. The network comprises an exactly symmetric block following a non-symmetric block, which we argue learns a transformation of the ground state analogous to quasiadiabatic continuation. Our work paves the way toward investigating quantum spin liquid problems within interpretable neural network architectures