Entanglement in spatially inhomogeneous many-fermion systems

Superfluid-Insulator Transition unambiguously detected by entanglement in one-dimensional disordered superfluids

We use entanglement to track the superfluid-insulator transition (SIT) in disordered fermionic superfluids described by the one-dimensional Hubbard model. Entanglement is found to have remarkable signatures of the SIT driven by i) the disorder strength V, ii) the concentration of impurities C and iii) the particle density n. Our results reveal the absence of a critical potential intensity on the SIT driven by V, i.e. any small V suffices to decrease considerably the degree of entanglement: it drops ∼50% for V = -0.25t. We also find that entanglement is non-monotonic with the concentration C, approaching to zero for a certain critical value CC. This critical concentration is found to be related to a special type of localization, here named as fully-localized state, which can be also reached for a particular density nC. Our results show that the SIT driven by n or C has distinct nature whether it leads to the full localization or to the ordinary one: it is a first-order quantum phase transition only when leading to full localization. In contrast, the SIT driven by V is never a first-order quantum phase transition independently on the type of localization reached.

Artificial neural networks for density-functional optimizations in fermionic systems

In this work we propose an artificial neural network functional to the ground-state energy of fermionic interacting particles in homogeneous chains described by the Hubbard model. Our neural network functional was proven to have an excellent performance: it deviates from numerically exact calculations by less than 0.15% for a vast regime of interactions and for all the regimes of filling factors and magnetizations. When compared to analytical functionals, the neural functional was found to be more precise for all the regimes of parameters, being particularly superior at the weakly interacting regime: where the analytical parametrization fails the most, ~7%, against only ~0.1% for the neural network. We have also applied our homogeneous functional to finite, localized impurities and harmonically confined systems within density-functional theory (DFT) methods. The results show that while our artificial neural network approach is substantially more accurate than other equivalently simple and fast DFT treatments, it has similar performance than more costly DFT calculations and other independent many-body calculations, at a fraction of the computational cost.