The authors systematically characterize the three-orbital Hubbard model using state-of-the-art determinant quantum Monte Carlo (DQMC) simulations with parameters relevant to the cuprate high-temperature superconductors. The DQMC results agree well with those from cuprate experiments, such as photoemission, and enable the identification of orbital content in the bands. A comparison of DQMC results to those from exact diagonalization and cluster perturbation theory elucidates how these different numerical techniques complement one another to produce a more complete understanding of the model and the cuprates.
The pseudogap regime of the cuprate high-temperature superconductors is characterized by a variety of competing orders, the nature of which are still widely debated. Recent experiments have provided evidence for electron nematic order, in which the electron fluid breaks rotational symmetry while preserving translational invariance. Raman spectroscopy, with its ability to symmetry resolve low energy excitations, is a unique tool that can be used to assess nematic fluctuations and nematic ordering tendencies. Here we compare results from determinant quantum Monte Carlo simulations of the Hubbard model to experimental results from Raman spectroscopy in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$, which show a prominent increase in the
B1g response around 10% hole doping as the temperature decreases, indicative of a rise in nematic fluctuations at low energy. Our results support a picture of nematic fluctuations with
B1g symmetry occurring in underdoped cuprates, which may arise from melted stripes at elevated temperatures.