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arXiv:2604.24883

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

W. Lou, Gino Cassella, Andres Perez Fadon, Halvard Sutterud, David Pfau, James S. Spencer, Johannes Knolle, W. M. C. Foulkes

Published Apr 27, 2026• 0 citations
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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.

DOI
10.48550/arxiv.2604.24883

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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.
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We probe the superconducting gap in the zero-temperature ground state of an attractively interacting spin-imbalanced two-dimensional Fermi gas with diffusion Monte Carlo simulations. A condensate fraction at nonzero pair momentum evinces a spatially nonuniform superconducting order parameter. Comparison with exact diagonalization studies confirms that the nonzero condensate fraction across a range of nonzero fermion pair momenta is consistent with nonexclusive pairing between majority and minority fermions, an extension beyond Fulde-Ferrell-Larkin-Ovchinnikov theory.
We present an extensive study of two-dimensional Larkin-Ovchinnikov (LO) superfluidity in a spin-imbalanced two-component atomic Fermi gas. In the context of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, we explore a wide and generic class of pairing gap functions with explicit spatial dependency. The mean-field theory of such phases is applied through the Bogoliubov-de Gennes equations in which the pairing gap can be determined self-consistently. To systematically explore the configuration space we consider both the canonical and grand canonical ensembles where we control the polarization or chemical potentials of the system, respectively. The mean-field calculations enable us to understand the nature of the phase transitions in the fully paired Bardeen-Cooper-Schrieffer (BCS) state, exotic LO phase, and partially polarized free Fermi gas (NPP{N}_{\text{PP}}NPP​). The order of the phase transitions has been examined and, in particular, we find a weak first-order phase transition between the exotic inhomogeneous LO phase and the BCS phase. In comparison to the three-dimensional case, where the phase diagram is dominated by a generic separation phase, we predict a broader parameter space for the spatially inhomogeneous LO phase. By computing the superfluid density of the LO phase at different polarization, we show how the superfluidity of the system is suppressed with increasing spin polarization.
Finite-momentum pairing, exemplified by Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, represents a paradigmatic form of unconventional superfluidity driven by Fermi-surface mismatch, but its detection in two-dimensional systems has remained elusive. Here we study a doped, spin-imbalanced attractive Hubbard model using a combined experimental and computational approach, based on quantum gas microscopy and constrained-path auxiliary-field quantum Monte Carlo, with direct comparisons showing quantitative agreement for short-range correlations at experimentally accessible temperatures. We identify broad regimes in density and magnetization where FFLO correlations emerge, and establish their finite-temperature evolution, with clear signatures of finite-momentum pairing already appearing at experimentally accessible temperatures. Spin-XY correlations are identified as a robust, directly measurable proxy for FFLO physics. Quantitative characterizations are obtained on the temperature dependence of a variety of observables and correlations, which elucidate the interplay of pairing with competing orders.