Abstract
We study the phase diagram of the Hubbard model in the limit where , the onsite repulsive interaction, is much smaller than the bandwidth. We present an asymptotically exact expression for , the superconducting transition temperature, in terms of the correlation functions of the noninteracting system which is valid for arbitrary densities so long as the interactions are sufficiently small. Our strategy for computing involves first integrating out all degrees of freedom having energy higher than an unphysical initial cutoff . Then, the renormalization group (RG) flows of the resulting effective action are computed and is obtained by determining the scale below which the RG flows in the Cooper channel diverge. We prove that is independent of . Using this method, we find a variety of unconventional superconducting ground states in two- and three-dimensional lattice systems, and present explicit results for and pairing symmetries as a function of the electron concentration.
10 More- Received 22 February 2010
DOI:https://doi.org/10.1103/PhysRevB.81.224505
©2010 American Physical Society
Erratum
Erratum: Superconductivity in the repulsive Hubbard model: An asymptotically exact weak-coupling solution [Phys. Rev. B 81, 224505 (2010)]
S. Raghu, S. A. Kivelson, and D. J. Scalapino
Phys. Rev. B 94, 219903 (2016)
Synopsis
Weak-coupling superconductivity from repulsive interactions
Published 11 June 2010
Rich physics emerges from an asymptotically exact solution of the weak-coupling limit of the Hubbard model.
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