Pairing in the two-dimensional Hubbard model from weak to strong coupling
Abstract
The Hubbard model is the simplest model that is believed to exhibit superconductivity arising from purely repulsive interactions, and has been extensively applied to explore a variety of unconventional superconducting systems. Here we study the evolution of the leading superconducting instabilities of the single-orbital Hubbard model on a two-dimensional square lattice as a function of onsite Coulomb repulsion U and band filling by calculating the irreducible particle-particle scattering vertex obtained from dynamical cluster approximation (DCA) calculations, and compare the results to both perturbative Kohn-Luttinger (KL) theory as well as the widely used random phase approximation (RPA) spin-fluctuation pairing scheme. Near half-filling we find remarkable agreement of the hierarchy of the leading pairing states between these three methods, implying adiabatic continuity between weak- and strong-coupling pairing solutions of the Hubbard model. The dx2-y2-wave instability is robust to increasing U near half-filling as expected. Away from half filling, the predictions of KL and RPA at small U for transitions to other pair states agree with DCA at intermediate U as well as recent diagrammatic Monte Carlo calculations. RPA results fail only in the very dilute limit, where it yields a dxy ground state instead of a p-wave state established by diagrammatic Montemore »
- Publication Date:
- Research Org.:
- Univ. of Florida, Gainesville, FL (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; Lundbeckfond fellowship
- OSTI Identifier:
- 1596391
- Alternate Identifier(s):
- OSTI ID: 1603796; OSTI ID: 1606663
- Grant/Contract Number:
- FG02-05ER46236; A9318; AC05-00OR22725
- Resource Type:
- Published Article
- Journal Name:
- Physical Review Research
- Additional Journal Information:
- Journal Name: Physical Review Research Journal Volume: 2 Journal Issue: 1; Journal ID: ISSN 2643-1564
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Pairing mechanisms; Superconducting order parameter; Superconductivity
Citation Formats
Rømer, Astrid T., Maier, Thomas A., Kreisel, Andreas, Eremin, Ilya, Hirschfeld, P. J., and Andersen, Brian M. Pairing in the two-dimensional Hubbard model from weak to strong coupling. United States: N. p., 2020.
Web. doi:10.1103/PhysRevResearch.2.013108.
Rømer, Astrid T., Maier, Thomas A., Kreisel, Andreas, Eremin, Ilya, Hirschfeld, P. J., & Andersen, Brian M. Pairing in the two-dimensional Hubbard model from weak to strong coupling. United States. doi:10.1103/PhysRevResearch.2.013108.
Rømer, Astrid T., Maier, Thomas A., Kreisel, Andreas, Eremin, Ilya, Hirschfeld, P. J., and Andersen, Brian M. Fri .
"Pairing in the two-dimensional Hubbard model from weak to strong coupling". United States. doi:10.1103/PhysRevResearch.2.013108.
@article{osti_1596391,
title = {Pairing in the two-dimensional Hubbard model from weak to strong coupling},
author = {Rømer, Astrid T. and Maier, Thomas A. and Kreisel, Andreas and Eremin, Ilya and Hirschfeld, P. J. and Andersen, Brian M.},
abstractNote = {The Hubbard model is the simplest model that is believed to exhibit superconductivity arising from purely repulsive interactions, and has been extensively applied to explore a variety of unconventional superconducting systems. Here we study the evolution of the leading superconducting instabilities of the single-orbital Hubbard model on a two-dimensional square lattice as a function of onsite Coulomb repulsion U and band filling by calculating the irreducible particle-particle scattering vertex obtained from dynamical cluster approximation (DCA) calculations, and compare the results to both perturbative Kohn-Luttinger (KL) theory as well as the widely used random phase approximation (RPA) spin-fluctuation pairing scheme. Near half-filling we find remarkable agreement of the hierarchy of the leading pairing states between these three methods, implying adiabatic continuity between weak- and strong-coupling pairing solutions of the Hubbard model. The dx2-y2-wave instability is robust to increasing U near half-filling as expected. Away from half filling, the predictions of KL and RPA at small U for transitions to other pair states agree with DCA at intermediate U as well as recent diagrammatic Monte Carlo calculations. RPA results fail only in the very dilute limit, where it yields a dxy ground state instead of a p-wave state established by diagrammatic Monte Carlo and low-order perturbative methods, as well as our DCA calculations. We discuss the origins of this discrepancy, highlighting the crucial role of the vertex corrections neglected in the RPA approach. Overall, comparison of the various methods over the entire phase diagram strongly suggests a smooth crossover of the superconducting interaction generated by local Hubbard interactions between weak and strong coupling.},
doi = {10.1103/PhysRevResearch.2.013108},
journal = {Physical Review Research},
number = 1,
volume = 2,
place = {United States},
year = {2020},
month = {1}
}
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DOI: 10.1103/PhysRevResearch.2.013108
DOI: 10.1103/PhysRevResearch.2.013108
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