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Understanding quantum many-body states of correlated electrons is one maintheme in modern condensed matter physics. Given that the Fermi-Hubbard model,the prototype of correlated electrons, has been recently realized in ultracoldoptical lattices, it is highly desirable to have controlled numericalmethodology to provide precise finite-temperature results upon doping, todirectly compare with experiments. Here, we demonstrate the exponential tensorrenormalization group (XTRG) algorithm [Phys. Rev. X 8, 031082 (2018)],complemented with independent determinant quantum Monte Carlo (DQMC) offer apowerful combination of tools for this purpose. XTRG provides full and accurateaccess to the density matrix and thus various spin and charge correlations,down to unprecedented low temperature of few percents of the fermion tunnelingenergy scale. We observe excellent agreement with ultracold fermionmeasurements at both half-filling and finite-doping, including thesign-reversal behavior in spin correlations due to formation of magneticpolarons, and the attractive hole-doublon and repulsive hole-hole pairs thatare responsible for the peculiar bunching and antibunching behavior of theantimoments.

Quantum Many-Body Simulations of the 2D Fermi-Hubbard Model in Ultracold Optical Lattices