Superconductivity in the repulsive Hubbard model: an asymptotically exact weak-coupling solution

Abstract

We study the phase diagram of the Hubbard model in the limit where U, the onsite repulsive interaction, is much smaller than the bandwidth. We present an asymptotically exact expression for T${}_c$, the superconducting transition temperature, in terms of the correlation functions of the non-interacting system which is valid for arbitrary densities so long as the interactions are sufficiently small. Our strategy for computing T${}_c$ involves first integrating out all degrees of freedom having energy higher than an unphysical initial cutoff ${\Omega }_0$. Then, the renormalization group (RG) flows of the resulting effective action are computed and T${}_c$ is obtained by determining the scale below which the RG flows in the Cooper channel diverge. We prove that T${}_c$ is independent of ${\Omega }_0$. Using this method, we find a variety of unconventional superconducting ground states in two and three dimensional lattice systems and present explicit results for T${}_c$ and pairing symmetries as a function of the electron concentration.

18 pages, 17 figures

References in corpus (30)

• Renormalization Group Approach to Interacting Fermions
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• The Nernst effect in high-$T_c$ superconductors
• Spin waves and electronic interactions in La2CuO4
• Weak Coupling Phase Diagram of the Two Chain Hubbard Model
• Renormalization group analysis of the 2D Hubbard model
• Resonating valence bonds and mean-field d-wave superconductivity in graphite
• Gaussian superconducting fluctuations, thermal transport, and the Nernst effect
• Exact SO(8) Symmetry in the Weakly-Interacting Two-Leg Ladder
• Entropy and Entanglement in Quantum Ground States
• Antiferromagnetically Driven Electronic Correlation in Iron Pnictides and Cuprates
• Mean-field theory for symmetry-breaking Fermi surface deformations on a square lattice
• The Superconducting Instabilities of the non half-filled Hubbard Model in Two Dimensions
• Testing the itinerancy of spin dynamics in superconducting Bi2212
• Formation of Electronic Nematic Phase in Interacting Systems
• Itinerant metamagnetism induced by electronic nematic order
• Renormalized perturbation theory for Fermi systems: Fermi surface deformation and superconductivity in the two-dimensional Hubbard model
• Renormalized mean-field analysis of antiferromagnetism and d-wave superconductivity in the two-dimensional Hubbard model
• Continuous renormalization for fermions and Fermi liquid theory
• Nernst effect and diamagnetism in phase fluctuating superconductors
• Flow to strong coupling in the two-dimensional Hubbard model
• Nernst effect in the vortex-liquid regime of a type-II superconductor
• Competing order, Fermi surface reconstruction, and quantum oscillations in underdoped high temperature superconductors
• Spin-triplet superconductivity in repulsive Hubbard models with disconnected Fermi surfaces: a case study on triangular and honeycomb lattices
• Tunneling Gap as Evidence for Time-Reversal Symmetry Breaking at Surfaces of High-Temperature Superconductors
• Interacting Electrons on a Square Fermi Surface
• Weakly interacting electrons and the renormalization group
• Third Order Perturbation Analysis of Pairing Symmetry in Two-Dimensional Hubbard Model
• Correlation functions for a two-dimensional electron system with bosonic interactions and a square Fermi surface
• Ferromagnetism and triplet superconductivity in the two-dimensional Hubbard model

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