Approximately-symmetric neural networks for quantum spin liquids

📅 2024-05-27
🏛️ arXiv.org
📈 Citations: 4
Influential: 0
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🤖 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.

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📝 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
Problem

Research questions and friction points this paper is trying to address.

Designing neural networks for quantum spin liquid problems
Outperforming symmetry-unaware architectures in quantum simulations
Exploring Hamiltonians with sign problems beyond existing methods
Innovation

Methods, ideas, or system contributions that make the work stand out.

Approximately-symmetric neural networks for spin liquids
Combines symmetric and non-symmetric blocks efficiently
Outperforms existing methods on large-scale quantum systems
D
Dominik S. Kufel
Department of Physics, Harvard University, 17 Oxford St. MA 02138, USA
J
Jack Kemp
Department of Physics, Harvard University, 17 Oxford St. MA 02138, USA
S
Simon M. Linsel
Faculty of Physics, Arnold Sommerfeld Centre for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstr. 37, 80333 München, Germany
C
C. Laumann
Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
N
Norman Y. Yao
Department of Physics, Harvard University, 17 Oxford St. MA 02138, USA