Pairing susceptibility of the two-dimensional Hubbard model in the thermodynamic limit

Abstract

We compute the diagrammatic expansion of the particle-particle susceptibility via algorithmic Matsubara integration and compute the correlated pairing susceptibility in the thermodynamic limit of the 2D Hubbard Model. We study the static susceptibility and its dependence on the pair momentum $\mathbf{q}$ for a range of temperature, interaction strength, and chemical potential. We show that $d_{x^2-y^2}$-wave pairing is expected in the model in the $U/t\to 0^{+}$ limit from direct perturbation theory. From this, we identify key second and third-order diagrams that support pairing processes and note that the diagrams responsible are not a part of charge or spin susceptibility expansions. We find two key components for pairing at momenta $(0,0)$ and $(\pi ,\pi )$ that can be well fit as separate bosonic modes. We extract amplitudes and correlation length scales where we find a predominantly local $(\pi ,\pi )$ pairing and non-local $\mathbf{q}=(0,0)$ pairs and present the relative weights of these modes for variation in temperature, doping, and interaction strength.

arXiv comment9 pages - 10 figures

References in corpus (27)

• A Common Thread: the pairing interaction for the unconventional superconductors
• Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
• Superconductivity and the Pseudogap in the two-dimensional Hubbard model
• Cluster Dynamical Mean Field Theory of the Mott Transition
• Local Electronic Correlation at the Two-Particle Level
• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• A Phenomenological Theory of the Anomalous Pseudogap Phase in Underdoped Cuprates
• Fluctuation diagnostics of the electron self-energy: Origin of the pseudogap physics
• Controlling Feynman diagrammatic expansions: physical nature of the pseudo gap in the two-dimensional Hubbard model
• Extended crossover from Fermi liquid to quasi-antiferromagnet in the half-filled 2D Hubbard model
• Energetics of superconductivity in the two dimensional Hubbard model
• Intertwined spin, charge and pair correlations in the two-dimensional Hubbard model in the thermodynamic limit
• Algorithmic Matsubara Integration for Hubbard-like models
• Pairing in the Two-Dimensional Hubbard Model from Weak to Strong Coupling
• Superconducting Fluctuations in the Normal State of the Two-Dimensional Hubbard Model
• Mechanism of Superconductivity in the Hubbard Model at Intermediate Interaction Strength
• Signatures of Fermi surface reconstruction in Raman spectra of underdoped cuprates
• Optimal grouping of arbitrary diagrammatic expansions via analytic pole structure
• Quantifying the role of antiferromagnetic fluctuations in the superconductivity of the doped Hubbard model
• Algorithmic approach to diagrammatic expansions for real-frequency evaluation of susceptibility functions
• Third Order Perturbation Analysis of Pairing Symmetry in Two-Dimensional Hubbard Model
• Single particle properties of the 2D Hubbard model for real frequencies at weak coupling: Breakdown of the Dyson series for partial self-energy expansions
• LIBAMI: Implementation of Algorithmic Matsubara Integration
• One- and two-particle properties of the weakly interacting two-dimensional Hubbard model in proximity to the van Hove singularity
• Fluctuation diagnostics of the finite temperature quasi-antiferromagnetic regime of the 2D Hubbard model
• Short-range charge fluctuations in the two-dimensional Hubbard model
• Mixed temperature-dependent order parameters in the extended Hubbard model

Cited by in corpus (2)

• Pairing susceptibility in the weakly interacting multilayer Hubbard model evaluated by direct perturbative expansion
• Computation Kernel for Feynman Diagrams