Variational Monte Carlo method for fermionic models combined with tensor networks and applications to the hole-doped two-dimensional Hubbard model

摘要

The conventional tensor-network states employ real-space product states as reference wave functions. Here,we propose a many-variable variationalMonte Carlo (mVMC) method combined with tensor networks by takingadvantages of both to study fermionic models. The variational wave function is composed of a pair productwave function operated by real-space correlation factors and tensor networks. Moreover, we can apply quantumnumber projections, such as spin, momentum, and lattice symmetry projections, to recover the symmetry ofthe wave function to further improve the accuracy. We benchmark our method for one- and two-dimensionalHubbard models, which show significant improvement over the results obtained individually either by mVMCor by tensor network. We have applied the present method to a hole-doped Hubbard model on the square lattice,which indicates the stripe charge/spin order coexisting with a weak d-wave superconducting order in the groundstate for the doping concentration of less than 0.3, where the stripe oscillation period gets longer with increasinghole concentration. The charge homogeneous and highly superconducting state also exists as a metastable excitedstate for the doping concentration less than 0.25.