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arXiv:2607.04168

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

Jianwei Gong, Junnian Xiong, Ruitao Xiao, Hui Li, Ziyu Li, H Huang, Dingping Li

Published Jul 5, 2026• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2607.04168

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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 64×6464\times6464×64, thereby enabling access to the thermodynamic limit. We find the key transition temperatures---namely the Néel temperature and the superconducting critical temperature TcT_cTc​---to be in quantitative agreement with experimental data. Above the ddd-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.
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We study the three-band Hubbard model for the cuprate superconductors using Quantum Monte Carlo simulations and the fluctuation exchange approximation including a self-consistent many-body renormalization of the single-particle propagator. The energy dispersion of the low-lying one-particle excitations is in very good agreement with spectroscopic measurements for a hole doping concentration δ = 0.25 of the CuO2 planes. At the same doping, we examine the spin susceptibility yielding a non-ordered phase with short-range incommensurate fluctuations near the antiferromagnetic wave vector. In the superconducting regime, the interaction vertex for the pairing correlation function in the extended s-wave channel shows a maximum for δ = 0.20, resembling the dependence of transition temperature Tc on doping.
Abstract The spectral properties of the doped t – t ’ Hubbard model, using parameters typical for high-temperature cuprate superconductors, and the mechanism of d-wave pairing remain among the longstanding problems of many-body fermionic materials. We used a strong-coupling Green’s function expansion around a correlated reference system, namely a particle-hole-symmetric undoped Hubbard lattice with t′=0{t}^{{\prime} }=0t′=0 t ′ = 0 , which can be treated numerically exactly using sign-problem-free lattice Quantum Monte Carlo calculations. This reference system exhibits a large antiferromagnetic Mott-Hubbard-Slater gap in the electronic spectrum. We investigate how the Mott-like spectrum is reconstructed under finite doping and nonzero t′{t}^{{\prime} }t′ t ′ using a dual-fermion-inspired perturbation expansion. For a large next-nearest-neighbor hopping t′=−0.3t{t}^{{\prime} }=-0.3tt′=−0.3t t ′ = − 0.3 t , characteristic of cuprate families with T c around 100 K, the electronic spectral function reveals a strongly renormalized flat-band feature with a pseudogap near the antinodal point. The superconducting response of this system to a small dx2−y2{d}_{{x}^{2}-{y}^{2}}dx2−y2​ d x 2 − y 2 -like external field shows a pseudogap at the antinodal point in the normal part of the Nambu Green’s function, associated with “bad-fermion” behavior in the normal phase. At the same time, the anomalous Green’s function exhibits a d-wave-like structure with zero response at the nodal point of the Brillouin zone.
The competition between ddd-wave superconductivity (SC) and antiferromagnetism (AF) in the high-Tc{T}_{c}Tc​ cuprates is investigated by studying the hole- and electron-doped two-dimensional Hubbard model with a recently proposed variational quantum-cluster theory. The approach is shown to provide a thermodynamically consistent determination of the particle number, provided that an overall shift of the on-site energies is treated as a variational parameter. The consequences for the single-particle excitation spectra and for the phase diagram are explored. By comparing the single-particle spectra with quantum Monte Carlo and experimental data, we verify that the low-energy excitations in a strongly correlated electronic system are described appropriately. The cluster calculations also reproduce the overall ground-state phase diagram of the high-temperature superconductors. In particular, they include salient features such as the enhanced robustness of the antiferromagnetic state as a function of electron doping and the tendency towards phase separation into a mixed antiferromagnetic-superconducting phase at low doping and a pure superconducting phase at high (both hole and electron) doping.
Proximity to a Mott insulating phase is likely to be an important physical ingredient of a theory that aims to describe high-temperature superconductivity in the cuprates. Quantum cluster methods are well suited to describe the Mott phase. Hence, as a step toward a quantitative theory of the competition between antiferromagnetism and ddd-wave superconductivity in the cuprates, we use cellular dynamical mean-field theory to compute zero-temperature properties of the two-dimensional square lattice Hubbard model. The ddd-wave order parameter is found to scale like the superexchange coupling JJJ for on-site interaction UUU comparable to or larger than the bandwidth. The order parameter also assumes a dome shape as a function of doping, while, by contrast, the gap in the single-particle density of states decreases monotonically with increasing doping. In the presence of a finite second neighbor hopping ${t}^{\ensuremath{'}}$, the zero-temperature phase diagram displays the electron-hole asymmetric competition between antiferromagnetism and superconductivity that is observed experimentally in the cuprates. Adding realistic third neighbor hopping ${t}^{\ensuremath{''}}$ improves the overall agreement with the experimental phase diagram. Since band parameters can vary depending on the specific cuprate considered, the sensitivity of the theoretical phase diagram to band parameters challenges the commonly held assumption that the doping vs Tc∕Tcmax{T}_{c}∕{T}_{c}^{\mathit{max}}Tc​∕Tcmax​ phase diagram of the cuprates is universal. The calculated angle-resolved photoemission spectrum displays the observed electron-hole asymmetry. The tendency to homogeneous coexistence of the superconducting and antiferromagnetic order parameters is stronger than observed in most experiments but consistent with many theoretical results and with experiments in some layered high-temperature superconductors. Clearly, our calculations reproduce important features of ddd-wave superconductivity in the cuprates that would otherwise be considered anomalous from the point of view of the standard Bardeen--Cooper--Schrieffer approach. At strong coupling, ddd-wave superconductivity and antiferromagnetism naturally appear as two equally important competing instabilities of the normal phase of the same underlying Hamiltonian.
One of the primary reasons that superconductivity in underdoped cuprates is enigmatic is that it emerges from an incoherent Fermi-arc state, so the applicability of the Bardeen-Cooper-Schrieffer (BCS) theory is questionable. Here we approach this problem by investigating unconventional ddd-wave superconductivity in a recently proposed solvable model for strongly correlated Fermi arcs. We show analytically that the exact incorporation of Fermi arcs fundamentally modifies the BCS equations, which enables us to isolate a many-body effect that suppresses the superconducting transition temperature TcT_cTc​ beyond the simple reduction expected from a shrinking Fermi surface. The theory unambiguously produces: (i) a TcT_cTc​ tracing out a dome as a function of hole doping, (ii) a new low-energy mode upon entering superconductivity, (iii) a suppressed superfluid stiffness in the underdoped regime, and (iv) a gap-to-TcT_cTc​ ratio far exceeding the BCS limit, all consistent with experimental observations in cuprate superconductors. These findings provide an analytic benchmark for understanding how superconductivity emerges from a correlated Fermi-arc state in high-TcT_cTc​ superconductors.