Sparse autoencoders applied to Neural Quantum States extract unsupervised features correlating with and causally steering physical observables such as order parameters while preserving variational energy.
Beyond Variational Bias: Resolving Intertwined Orders in the Hubbard Model
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abstract
The two-dimensional Hubbard model at finite doping hosts competing or intertwined orders, resulting in conflicting conclusions from different computational approaches regarding its ground state. We show that a key source of such discrepancies is the bias encoded in the variational ansatz. We consider three different Transformer backflow fermionic wave functions based on a Slater determinant, its particle-hole counterpart, and a Pfaffian, initialized without any mean-field pretraining. We show that, despite achieving nearly degenerate, state-of-the-art variational energies, each ansatz converges to a state with qualitatively different spin, charge, and pairing correlations. Upon improving accuracy via symmetry restoration and variance reduction, however, all three converge to the same physical picture: coexisting superconducting and stripe orders. These results demonstrate that variational energy alone is insufficient to identify the ground state in the presence of competing phases, and highlight the importance of tracking how correlation functions evolve as the wave function is systematically improved before drawing physical conclusions.
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2026 3verdicts
UNVERDICTED 3representative citing papers
Real-time dynamics in the 2D Hubbard model show thermalization of double occupancy below a critical U_c but clear breakdown of thermalization above it.
Transformer wave functions for the J1-J2 Heisenberg model exhibit size-independent power-law decay of V-score with compute, with the exponent decreasing as frustration increases.
citing papers explorer
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Mechanistic Interpretability and Causal Feature Steering of Neural Quantum States via Sparse Autoencoders
Sparse autoencoders applied to Neural Quantum States extract unsupervised features correlating with and causally steering physical observables such as order parameters while preserving variational energy.
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Breakdown of Thermalization from Real-Time Dynamics in the Two-Dimensional Hubbard Model
Real-time dynamics in the 2D Hubbard model show thermalization of double occupancy below a critical U_c but clear breakdown of thermalization above it.
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Scaling Laws for Neural-Network Quantum States
Transformer wave functions for the J1-J2 Heisenberg model exhibit size-independent power-law decay of V-score with compute, with the exponent decreasing as frustration increases.