Approximately-symmetric neural networks for quantum spin liquids

TL;DR

This paper introduces approximately-symmetric neural networks tailored for quantum spin liquids, demonstrating superior performance and scalability over existing methods, and enabling exploration of complex Hamiltonians with sign problems.

Contribution

The authors develop a novel neural network architecture that is both parameter-efficient and scalable, specifically designed for quantum spin liquid problems, outperforming prior symmetry-unaware models.

Findings

Outperforms existing neural network architectures in quantum spin liquid tasks.

Enables exploration of Hamiltonians with sign problems beyond traditional methods.

Demonstrates effectiveness on large system sizes up to N=1584.

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 outperform existing symmetry-unaware neural network architectures. Utilizing the mixed-field toric code and PXP Rydberg Hamiltonian models, 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 for toric code, N=1584 for Rydberg PXP), 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.