Simulating the Fermi-Hubbard model with bosonic tensor network states

Tensor network states, such as projected entangled pair states (PEPS), are becoming a powerful tool to simulate 2D strongly correlated systems. Although fermionic tensor networks are widely used, an open question in the field is whether we can efficiently simulate fermion systems with bosonic tensor networks, such as bosonic PEPS, using appropriate fermion-to-qubit mappings, which is more similar in spirit to proposed simulations on quantum devices. Critical questions related to the ease of optimizing such bosonic ansatz remain. In this work, we develop a bosonic PEPS algorithm to simulate the Fermi-Hubbard model, which is mapped to a non-local spin system by a Jordan-Wigner transformation. We compare the results obtained using both fermion and bosonic PEPS, discuss their performance and the possibilities for future improvement.