Attention is all you need to solve chiral superconductivity

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.