We employ the nonperturbative many-body spin GW method to compute the single-particle Green's function, and the covariance method to evaluate the two-body correlation functions, for the Hubbard model of superconductors. The method, benchmarked at strong coupling and low temperatures, allows simulations on lattices up to $64\times64$ , thereby enabling access to the thermodynamic limit. We find the key transition temperatures---namely the Néel temperature and the superconducting critical temperature $T_c$ ---to be in quantitative agreement with experimental data. Above the $d$ -wave superconducting dome, there exists a broad pseudogap region in which the normal-state excitations are suppressed. These results indicate our approach may offer a new route toward investigating strongly correlated systems, especially cuprate superconductors.We employ the nonperturbative many-body spin GW method to compute the single-particle Green's function, and the covariance method to evaluate the two-body correlation functions, for the Hubbard model of superconductors. The method, benchmarked at strong coupling and low temperatures, allows simulations on lattices up to $64\times64$, thereby enabling access to the thermodynamic limit. We find the key transition temperatures---namely the Néel temperature and the superconducting critical temperature $T_c$---to be in quantitative agreement with experimental data. Above the $d$-wave superconducting dome, there exists a broad pseudogap region in which the normal-state excitations are suppressed. These results indicate our approach may offer a new route toward investigating strongly correlated systems, especially cuprate superconductors.

arXiv:2607.04168Jul 5, 20260 citations

Application of many-body nonperturbative theories to the three-dimensional attractive Hubbard model

Junnian Xiong, Hui Li, Yingze Su +1 more

The attractive Fermi-Hubbard model stands out as a simple model for studying the pairing and superconductivity of fermions on a lattice. In this article, we apply several many-body theories in the three-dimensional attractive Hubbard model. Specifically, we compare the results of various GW methods with DQMC simulations and observe that they provide reliable results in the weak to intermediate coupling regime. The critical exponents also agree well with the accurate results obtained from the 3D XY model. In the superconducting phase, the post-GW method significantly improves the description of Green's functions and density of states. Additionally, we propose a method to determine the temperature at which the pseudogap appears.The attractive Fermi-Hubbard model stands out as a simple model for studying the pairing and superconductivity of fermions on a lattice. In this article, we apply several many-body theories in the three-dimensional attractive Hubbard model. Specifically, we compare the results of various GW methods with DQMC simulations and observe that they provide reliable results in the weak to intermediate coupling regime. The critical exponents also agree well with the accurate results obtained from the 3D XY model. In the superconducting phase, the post-GW method significantly improves the description of Green's functions and density of states. Additionally, we propose a method to determine the temperature at which the pseudogap appears.

arXiv:2502.11527Physical review. B./Physical review. BJul 23, 20252 citations

64\times64

, thereby enabling access to the thermodynamic limit. We find the key transition temperatures---namely the Néel temperature and the superconducting critical temperature

T_c

---to be in quantitative agreement with experimental data. Above the

d

-wave superconducting dome, there exists a broad pseudogap region in which the normal-state excitations are suppressed. These results indicate our approach may offer a new route toward investigating strongly correlated systems, especially cuprate superconductors.