Investigation of the Hubbard model with finite fermion projected entangled pair state

The Hubbard model stands as a cornerstone in theoretical condensed matter physics for understanding strong electron correlations and emergent phenomena such as magnetism and superconductivity. In this work, we employ large-scale numerical simulations based on the finite fermionic projected entangled-pair states (PEPS) method to investigate the ground-state properties of the Hubbard model with next-nearest-neighbour hopping. Our results reveal the competition among various orders and offer key insights into the mechanism of superconductivity within this paradigmatic model.