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The Hubbard model is a longstanding problem in the theory of stronglycorrelated electrons and a very active one in the experiments with ultracoldfermionic atoms. Motivated by current and prospective quantum simulations, weapply a two-dimensional tensor network, an infinite projected entangled pairstate, evolved in imaginary time by the neighborhood tensor update algorithmworking directly in the thermodynamic limit. With U(1)xU(1) symmetry and thebond dimensions up to 29, we generate thermal states down to the temperature of0.17 times the hopping rate. We obtain results for spin and charge correlators,unaffected by boundary effects. The spin correlators, measurable in prospectiveultracold atoms experiments attempting to approach the thermodynamic limit,provide evidence of disruption of the antiferromagnetic background with mobileholes in a slightly doped Hubbard model. The charge correlators reveal thepresence of hole-doublon pairs near half filling and signatures of hole-holerepulsion on doping. We also obtain specific heat in the slightly doped regime.

Finite temperature tensor network study of the Hubbard model on an infinite square lattice