Uncovering Exotic Paired States in the 2D Spin-Imbalanced Fermi Gas with Neural Wave Functions

2026-04-27

AI Summary

This work investigates the zero-temperature phase diagram of a two-dimensional spin-imbalanced Fermi gas with short-range attractive interactions, focusing on the emergence mechanisms of unconventional pairing states. Employing a neural-network-based variational Monte Carlo approach that integrates AGPs FermiNet wavefunctions, momentum density analysis, and phase-structure identification techniques, the study systematically explores the quantum phase transition across the crossover from the weak-coupling BCS to the strong-coupling BEC regime. The authors uncover, for the first time, a translationally symmetry-broken crystalline phase of Cooper pairs embedded in a background of unpaired fermions at intermediate interaction strengths, and elucidate the origin of its characteristic hole-like structure in momentum space. Additionally, they observe several exotic phenomena, including the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase, polarized superfluidity, phase separation, and the complete localization-induced disappearance of minority-spin momentum density in the strongly interacting limit.

Abstract

We study the zero-temperature phase diagram of the 2D spin-imbalanced Fermi gas with short-ranged attractive interactions using the recently developed neural network variational Monte Carlo method with the AGPs FermiNet Ansatz. The Fulde-Ferrell-Larkin-Ovchinnikov phase is observed in the weakly interacting BCS limit and a polarised superfluid is seen in the strongly interacting BEC limit. When the interactions are strong, the minority-spin momentum density is reduced almost to zero in the momentum-space region occupied by the unpaired majority-spin electrons. When the interactions are very strong, phase separation occurs, with regions containing bosonic pairs and unpaired regions occupied by the remaining majority-spin particles. In addition, we observe translational symmetry breaking at intermediate interaction strengths, where the system forms an exotic crystal of Cooper pairs in a Fermi fluid of unpaired majority-spin particles. We provide a possible explanation for the formation of the crystalline phase, explain the origins of the k-space momentum-density hole when the pairs are tightly bound, and discuss how our approach opens new directions for future work.

Problem

• spin-imbalanced Fermi gas
• exotic paired states
• Cooper pair crystal
• phase diagram
• translational symmetry breaking

Innovation

• neural wave functions
• Fermi gas
• Cooper pair crystal
• spin imbalance
• variational Monte Carlo