Fermi Sets achieve universal approximation of fermionic wavefunctions using K antisymmetric bases times symmetric neural networks, where K equals 1 in 1D, 2 in 2D, and grows linearly with particle number in higher dimensions.
Attention is all you need to solve chiral superconductivity
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abstract
Recent advances on neural quantum states have shown that correlations between quantum particles can be efficiently captured by attention -- a foundation of modern neural architectures that enables neural networks to learn the relation between objects. In this work, we show that a general-purpose self-attention Fermi neural network is able to find chiral $p_x \pm ip_y$ superconductivity in an attractive Fermi gas by energy minimization, without prior knowledge or bias towards pairing. The superconducting state is identified from the optimized wavefunction by measuring various physical observables. We develop a symmetry projection method that reveals the ground state angular momentum and time-reversal symmetry breaking, and a computation of the full two-body reduced density matrix spectrum that reveals the off-diagonal long-range order due to the dominant chiral $p$-wave pairing channel. Our work paves the way for AI-driven discovery of unconventional and topological superconductivity in strongly correlated quantum materials.
fields
cond-mat.str-el 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
A learnable Gaussian basis transformation lowers variational energies in neural-network variational Monte Carlo for the three-dimensional homogeneous electron gas.
citing papers explorer
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Fermi Sets: Universal and interpretable neural architectures for fermions
Fermi Sets achieve universal approximation of fermionic wavefunctions using K antisymmetric bases times symmetric neural networks, where K equals 1 in 1D, 2 in 2D, and grows linearly with particle number in higher dimensions.
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Enhancing Neural-Network Variational Monte Carlo through Basis Transformation
A learnable Gaussian basis transformation lowers variational energies in neural-network variational Monte Carlo for the three-dimensional homogeneous electron gas.