Gino Cassella

Wan Tong Lou, Gino Cassella, Andres Perez Fadon et al.

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.

Adam Foster, Zeno Schätzle, P. Bernát Szabó et al. · microsoft-research

Reliable description of bond breaking remains a major challenge for quantum chemistry due to the multireferential character of the electronic structure in dissociating species. Multireferential methods in particular suffer from large computational cost, which under the normal paradigm has to be paid anew for each system at a full price, ignoring commonalities in electronic structure across molecules. Quantum Monte Carlo with deep neural networks (deep QMC) uniquely offers to exploit such commonalities by pretraining transferable wavefunction models, but all such attempts were so far limited in scope. Here, we bring this new paradigm to fruition with Orbformer, a novel transferable wavefunction model pretrained on 22,000 equilibrium and dissociating structures that can be fine-tuned on unseen molecules reaching an accuracy-cost ratio rivalling classical multireferential methods. On established benchmarks as well as more challenging bond dissociations and Diels-Alder reactions, Orbformer is the only method that consistently converges to chemical accuracy (1 kcal/mol). This work turns the idea of amortizing the cost of solving the Schrödinger equation over many molecules into a practical approach in quantum chemistry.

Wan Tong Lou, Halvard Sutterud, Gino Cassella et al.

Understanding superfluidity remains a major goal of condensed matter physics. Here we tackle this challenge utilizing the recently developed Fermionic neural network (FermiNet) wave function Ansatz [D. Pfau et al., Phys. Rev. Res. 2, 033429 (2020).] for variational Monte Carlo calculations. We study the unitary Fermi gas, a system with strong, short-range, two-body interactions known to possess a superfluid ground state but difficult to describe quantitatively. We demonstrate key limitations of the FermiNet Ansatz in studying the unitary Fermi gas and propose a simple modification based on the idea of an antisymmetric geminal power singlet (AGPs) wave function. The new AGPs FermiNet outperforms the original FermiNet significantly in paired systems, giving results which are more accurate than fixed-node diffusion Monte Carlo and are consistent with experiment. We prove mathematically that the new Ansatz, which only differs from the original Ansatz by the method of antisymmetrization, is a strict generalization of the original FermiNet architecture, despite the use of fewer parameters. Our approach shares several advantages with the original FermiNet: the use of a neural network removes the need for an underlying basis set; and the flexibility of the network yields extremely accurate results within a variational quantum Monte Carlo framework that provides access to unbiased estimates of arbitrary ground-state expectation values. We discuss how the method can be extended to study other superfluids.