arXiv subjects

Junnian Xiong

Publications and source records attributed to Junnian Xiong.

4 recordsLinked to original sources

arXiv2026

Cuprate d-wave superconductivity based on Non perturbative many body theory for spin fluctuation

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.

cond-mat.str-el↗

arXiv2026

Nonpertubative Many-Body Theory for the Two-Dimensional Hubbard Model at Low Temperature: From Weak to Strong Coupling Regimes

In theoretical studies of two-dimensional (2D) systems, the Mermin-Wagner theorem prevents continuous symmetry breaking at any finite temperature, thus forbidding a Landau phase transition at a critical temperature $T_c$. The difficulty arises when many-body theoretical studies predict a Landau phase transition at finite temperatures, which contradicts the Mermin-Wagner theorem and is termed a pseudo phase transition. To tackle this problem, we systematically develop a symmetrization scheme, defined as averaging physical quantities over all symmetry-breaking states, thus ensuring that it preserves the Mermin-Wagner theorem. We apply the symmetrization scheme to the GW-covariance calculation for the 2D repulsive Hubbard model at half-filling in the intermediate-to-strong coupling regime and at low temperatures, obtaining the one-body Green's function and spin-spin correlation function, and benchmark them against Determinant Quantum Monte Carlo (DQMC) with good agreement.The spin-spin correlation functions are approached within the covariance theory, a general method for calculating two-body correlation functions from a one-particle starting point, such as the GW formalism used here, which ensures the preservation of the fundamental fluctuation-dissipation relation (FDR) and Ward-Takahashi identities (WTI). With the FDR and WTI satisfied, we conjecture that the $χ$-sum rule, a fundamental relation from the Pauli exclusion principle, can be used to probe the reliability of many-body methods, and demonstrate this by comparing the GW-covariance and mean-field-covariance approaches. This work provides a novel framework to investigate the strong-coupling and doped regime of the 2D Hubbard model, which is believed to be applicable to real high-$T_c$ cuprate superconductors.

cond-mat.str-el↗

arXiv2025

Application of Many-body Non-perturbative Theories to the Three-Dimensional Attractive Hubbard Model

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.

cond-mat.str-el↗

arXiv2024

Post-$GW$ theory and its application to pseudogap in strongly correlated system

The $GW$ approximation is a widely used framework for studying correlated materials, but it struggles with certain limitations, such as its inability to explain pseudogap phenomena. To overcome these problems, we propose a systematic theoretical framework for Green's function corrections and apply it specifically to the $GW$ approximation. In this new theory, the screened potential is reconnected to the physical response function, i.e. the covariant response function proposed in \cite{cGW_2023}, rather than using the RPA formula. We apply our scheme to calculate Green's function, the spectral function, and the charge compressibility in the two-dimensional Hubbard model. Our scheme yields significant qualitative and quantitative improvements over the standard $GW$ method and successfully captures the pseudogap behavior.

cond-mat.str-el↗