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. https://doi.org/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. https://doi.org/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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Works referenced in this record:
Spin susceptibility representation of the pairing interaction for the two-dimensional Hubbard model
journal, April 2007
- Maier, T. A.; Jarrell, M.; Scalapino, D. J.
- Physical Review B, Vol. 75, Issue 13
Phase diagram of the t – U 2 Hamiltonian of the weak coupling Hubbard model
journal, February 2008
- Yanagisawa, Takashi
- New Journal of Physics, Vol. 10, Issue 2
Antiferromagnetic to superconducting phase transition in the hole- and electron-doped Hubbard model at zero temperature
journal, July 2006
- Aichhorn, M.; Arrigoni, E.; Potthoff, M.
- Physical Review B, Vol. 74, Issue 2
Pairing symmetry of the one-band Hubbard model in the paramagnetic weak-coupling limit: A numerical RPA study
journal, September 2015
- Rømer, A. T.; Kreisel, A.; Eremin, I.
- Physical Review B, Vol. 92, Issue 10
Two-particle correlations in a dynamic cluster approximation with continuous momentum dependence: Superconductivity in the two-dimensional Hubbard model
journal, May 2014
- Staar, Peter; Maier, Thomas; Schulthess, Thomas C.
- Physical Review B, Vol. 89, Issue 19
Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory
journal, January 2016
- Zheng, Bo-Xiao; Chan, Garnet Kin-Lic
- Physical Review B, Vol. 93, Issue 3
Mechanism for Unconventional Superconductivity in the Hole-Doped Rashba-Hubbard Model
journal, April 2018
- Greco, Andrés; Schnyder, Andreas P.
- Physical Review Letters, Vol. 120, Issue 17
Strongly correlated superconductivity: A plaquette dynamical mean-field theory study
journal, September 2007
- Haule, Kristjan; Kotliar, Gabriel
- Physical Review B, Vol. 76, Issue 10
Pairing instabilities in the two-dimensional Hubbard model
journal, November 1992
- Chubukov, Andrey V.; Lu, Jian Ping
- Physical Review B, Vol. 46, Issue 17
Spin-fluctuation mechanism of superconductivity in cuprates
journal, July 2005
- Prelovšek, P.; Ramšak, A.
- Physical Review B, Vol. 72, Issue 1
Superfluidity of Low-Density Fermion Systems
journal, January 1968
- Fay, D.; Layzer, A.
- Physical Review Letters, Vol. 20, Issue 5
-wave pairing in lightly doped Mott insulators
journal, February 2005
- Plekhanov, Evgeny; Becca, Federico; Sorella, Sandro
- Physical Review B, Vol. 71, Issue 6
d -wave superconductivity in the presence of nearest-neighbor Coulomb repulsion
journal, May 2018
- Jiang, M.; Hähner, U. R.; Schulthess, T. C.
- Physical Review B, Vol. 97, Issue 18
Effect of Ferromagnetic Spin Correlations on Superconductivity
journal, August 1966
- Berk, N. F.; Schrieffer, J. R.
- Physical Review Letters, Vol. 17, Issue 8
A possible origin for heavy Fermion superconductivity
journal, October 1986
- Cyrot, M.
- Solid State Communications, Vol. 60, Issue 3
Quantum cluster theories
journal, October 2005
- Maier, Thomas; Jarrell, Mark; Pruschke, Thomas
- Reviews of Modern Physics, Vol. 77, Issue 3
Ground-state phase diagram of the repulsive fermionic Hubbard model on the square lattice from weak coupling
journal, August 2016
- Šimkovic, Fedor; Liu, Xuan-Wen; Deng, Youjin
- Physical Review B, Vol. 94, Issue 8
Continuous-time Monte Carlo methods for quantum impurity models
journal, May 2011
- Gull, Emanuel; Millis, Andrew J.; Lichtenstein, Alexander I.
- Reviews of Modern Physics, Vol. 83, Issue 2
Stripe and superconducting order competing in the Hubbard model on a square lattice studied by a combined variational Monte Carlo and tensor network method
journal, November 2018
- Darmawan, Andrew S.; Nomura, Yusuke; Yamaji, Youhei
- Physical Review B, Vol. 98, Issue 20
High- superconductors: A variational theory of the superconducting state
journal, August 2004
- Paramekanti, Arun; Randeria, Mohit; Trivedi, Nandini
- Physical Review B, Vol. 70, Issue 5
Binding of holes in one-band models of oxide superconductors
journal, May 1989
- Riera, J. A.; Young, A. P.
- Physical Review B, Vol. 39, Issue 13
Structure of the Pairing Interaction in the Two-Dimensional Hubbard Model
journal, February 2006
- Maier, T. A.; Jarrell, M. S.; Scalapino, D. J.
- Physical Review Letters, Vol. 96, Issue 4
Dynamics of the Pairing Interaction in the Hubbard and Models of High-Temperature Superconductors
journal, June 2008
- Maier, T. A.; Poilblanc, D.; Scalapino, D. J.
- Physical Review Letters, Vol. 100, Issue 23
Competition between Antiferromagnetism and Superconductivity in High- Cuprates
journal, April 2005
- Sénéchal, David; Lavertu, P. -L.; Marois, M. -A.
- Physical Review Letters, Vol. 94, Issue 15
Susceptibility and Effective Interaction in the Dilute Two Dimensional Hubbard Model
journal, January 1999
- Takahashi, Hideaki
- Journal of the Physical Society of Japan, Vol. 68, Issue 1
Spin-fluctuation-mediated even-parity pairing in heavy-fermion superconductors
journal, November 1986
- Miyake, K.; Schmitt-Rink, S.; Varma, C. M.
- Physical Review B, Vol. 34, Issue 9
Magnetic and Superconducting Instabilities of the Hubbard Model at the Van Hove Filling
journal, October 2001
- Honerkamp, Carsten; Salmhofer, Manfred
- Physical Review Letters, Vol. 87, Issue 18
Antiferromagnetically driven electronic correlations in iron pnictides and cuprates
journal, August 2009
- Zhai, Hui; Wang, Fa; Lee, Dung-Hai
- Physical Review B, Vol. 80, Issue 6
The Resonating Valence Bond State in La2CuO4 and Superconductivity
journal, March 1987
- Anderson, P. W.
- Science, Vol. 235, Issue 4793
Stripe order in the underdoped region of the two-dimensional Hubbard model
journal, November 2017
- Zheng, Bo-Xiao; Chung, Chia-Min; Corboz, Philippe
- Science, Vol. 358, Issue 6367
Metallic and insulating stripes and their relation with superconductivity in the doped Hubbard model
journal, January 2019
- Tocchio, Luca Fausto; Montorsi, Arianna; Becca, Federico
- SciPost Physics, Vol. 7, Issue 2
Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
journal, December 2015
- LeBlanc, J. P. F.; Antipov, Andrey E.; Becca, Federico
- Physical Review X, Vol. 5, Issue 4
Superconductivity in the repulsive Hubbard model: An asymptotically exact weak-coupling solution
journal, June 2010
- Raghu, S.; Kivelson, S. A.; Scalapino, D. J.
- Physical Review B, Vol. 81, Issue 22
Superconductivity in electron-doped cuprates: Gap shape change and symmetry crossover with doping
journal, February 2004
- Guinea, Francisco; Markiewicz, Robert S.; Vozmediano, María A. H.
- Physical Review B, Vol. 69, Issue 5
Competition among various charge-inhomogeneous states and d -wave superconducting state in Hubbard models on square lattices
journal, January 2018
- Ido, Kota; Ohgoe, Takahiro; Imada, Masatoshi
- Physical Review B, Vol. 97, Issue 4
Effects of longer-range interactions on unconventional superconductivity
journal, January 2012
- Raghu, S.; Berg, E.; Chubukov, A. V.
- Physical Review B, Vol. 85, Issue 2
Superconductivity of the Two-Dimensional Hubbard Model with a Small U
journal, March 2001
- Kondo, Jun
- Journal of the Physical Society of Japan, Vol. 70, Issue 3
Strong Coupling Superconductivity, Pseudogap, and Mott Transition
journal, May 2012
- Sordi, G.; Sémon, P.; Haule, K.
- Physical Review Letters, Vol. 108, Issue 21
Superconductivity in the two-dimensional t - t ′ -Hubbard model
journal, January 2014
- Eberlein, Andreas; Metzner, Walter
- Physical Review B, Vol. 89, Issue 3
Stripe order from the perspective of the Hubbard model
journal, April 2018
- Huang, Edwin W.; Mendl, Christian B.; Jiang, Hong-Chen
- npj Quantum Materials, Vol. 3, Issue 1
Third Order Perturbation Analysis of Pairing Symmetry in Two-Dimensional Hubbard Model
journal, June 2002
- Fukazawa, Hirono; Yamada, Kosaku
- Journal of the Physical Society of Japan, Vol. 71, Issue 6
Mean-field theory of high- superconductivity: The superexchange mechanism
journal, July 1987
- Ruckenstein, Andrei E.; Hirschfeld, Peter J.; Appel, J.
- Physical Review B, Vol. 36, Issue 1
d - and p -Wave Superconductivity Mediated by Spin Fluctuations in Two- and Three-Dimensional Single-Band Repulsive Hubbard Model
journal, April 2000
- Arita, Ryotaro; Kuroki, Kazuhiko; Aoki, Hideo
- Journal of the Physical Society of Japan, Vol. 69, Issue 4
New Mechanism for Superconductivity
journal, September 1965
- Kohn, W.; Luttinger, J. M.
- Physical Review Letters, Vol. 15, Issue 12
Superconducting Phase Diagram of the Paramagnetic One-Band Hubbard Model
journal, September 2016
- Kreisel, Andreas; Rømer, Astrid T.; Hirschfeld, P. J.
- Journal of Superconductivity and Novel Magnetism, Vol. 30, Issue 1
Kohn-Luttinger effect and the instability of a two-dimensional repulsive Fermi liquid at T =0
journal, July 1993
- Chubukov, Andrey V.
- Physical Review B, Vol. 48, Issue 2
Dynamical mean-field theory study of stripe order and d -wave superconductivity in the two-dimensional Hubbard model
journal, February 2018
- Vanhala, Tuomas I.; Törmä, Päivi
- Physical Review B, Vol. 97, Issue 7
Emergent BCS regime of the two-dimensional fermionic Hubbard model: Ground-state phase diagram
journal, June 2015
- Deng, Youjin; Kozik, Evgeny; Prokof'ev, Nikolay V.
- EPL (Europhysics Letters), Vol. 110, Issue 5
D-wave pairing in the two-dimensional Hubbard model with low filling
journal, June 1992
- Baranov, M. A.; Kagan, M. Yu.
- Zeitschrift f�r Physik B Condensed Matter, Vol. 86, Issue 2
Superconductivity from repulsive interaction
conference, January 2013
- Maiti, Saurabh; Chubukov, Andrey V.
- LECTURES ON THE PHYSICS OF STRONGLY CORRELATED SYSTEMS XVII: Seventeenth Training Course in the Physics of Strongly Correlated Systems, AIP Conference Proceedings
Superconducting instabilities of the non-half-filled Hubbard model in two dimensions
journal, October 1996
- Zanchi, D.; Schulz, H. J.
- Physical Review B, Vol. 54, Issue 13
Conserving Approximations for Strongly Correlated Electron Systems: Bethe-Salpeter Equation and Dynamics for the Two-Dimensional Hubbard Model
journal, February 1989
- Bickers, N. E.; Scalapino, D. J.; White, S. R.
- Physical Review Letters, Vol. 62, Issue 8
Superconductivity and the Pseudogap in the Two-Dimensional Hubbard Model
journal, May 2013
- Gull, Emanuel; Parcollet, Olivier; Millis, Andrew J.
- Physical Review Letters, Vol. 110, Issue 21
Superexchange mechanism and d -wave superconductivity
journal, September 1988
- Kotliar, Gabriel; Liu, Jialin
- Physical Review B, Vol. 38, Issue 7
Antiferromagnetic spin fluctuation and superconductivity
journal, July 2003
- Moriya, T. ru; Ueda, Kazuo
- Reports on Progress in Physics, Vol. 66, Issue 8
Magnetism and superconductivity in the model
journal, January 2008
- Spanu, Leonardo; Lugas, Massimo; Becca, Federico
- Physical Review B, Vol. 77, Issue 2
Superconductivity in the Two-Dimensional Model
journal, February 2002
- Sorella, S.; Martins, G. B.; Becca, F.
- Physical Review Letters, Vol. 88, Issue 11
-Wave Superconductivity and Pomeranchuk Instability in the Two-Dimensional Hubbard Model
journal, December 2000
- Halboth, Christoph J.; Metzner, Walter
- Physical Review Letters, Vol. 85, Issue 24
A common thread: The pairing interaction for unconventional superconductors
journal, October 2012
- Scalapino, D. J.
- Reviews of Modern Physics, Vol. 84, Issue 4
Phase diagram of the weak-coupling two-dimensional Hubbard model at low and intermediate electron density
journal, April 1999
- Hlubina, Richard
- Physical Review B, Vol. 59, Issue 14
Antagonistic effects of nearest-neighbor repulsion on the superconducting pairing dynamics in the doped Mott insulator regime
journal, October 2016
- Reymbaut, A.; Charlebois, M.; Asiani, M. Fellous
- Physical Review B, Vol. 94, Issue 15
-wave pairing near a spin-density-wave instability
journal, December 1986
- Scalapino, D. J.; Loh, E.; Hirsch, J. E.
- Physical Review B, Vol. 34, Issue 11
Breakdown of the Landau-Fermi liquid in two dimensions due to umklapp scattering
journal, January 2001
- Honerkamp, C.; Salmhofer, M.; Furukawa, N.
- Physical Review B, Vol. 63, Issue 3
Resilience of -wave superconductivity to nearest-neighbor repulsion
journal, February 2013
- Sénéchal, D.; Day, A. G. R.; Bouliane, V.
- Physical Review B, Vol. 87, Issue 7
Superconductivity in the two-dimensional Hubbard model
journal, November 1995
- Beenen, J.; Edwards, D. M.
- Physical Review B, Vol. 52, Issue 18