We demonstrate the use of finite-size fermionic projected entangled pair states, in conjunction with variational Monte Carlo, to perform accurate simulations of the ground state of the 2D Hubbard model. Using bond dimensions of up to $D=28$, we show that we can surpass state-of-the-art density matrix renormalization group energies that use up to $m=32000$ SU(2) multiplets on eight-leg ladders. We further apply our methodology to $10\times 16$, $12\times 16$, and $16\times 16$ lattices at $1/8$ hole doping and observe the dimensional crossover between stripe orientations. Our Letter shows the power of finite-size fermionic tensor networks to resolve the physics of the 2D Hubbard model and related problems.

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• Quantum simulation
• Hubbard model
• Projected entangled pair states
• Tensor network methods
• Tensor network renormalization