Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2205.06286 · Proceedings of the National Academy of Sciences

Mechanism of superconductivity in the Hubbard model at intermediate interaction strength

Xinyang Dong, Lorenzo Del Re, A. Toschi, Emanuel Gull

Published Aug 10, 2022• 45 citations
arXivHTMLPDF

Abstract

We study the fluctuations responsible for pairing in the d -wave superconducting state of the two-dimensional Hubbard model at intermediate coupling within a cluster dynamical mean-field theory with a numerically exact quantum impurity solver. By analyzing how momentum- and frequency-dependent fluctuations generate the d -wave superconducting state in different representations, we identify antiferromagnetic fluctuations as the pairing glue of superconductivity in both the underdoped and the overdoped regime. Nevertheless, in the intermediate coupling regime, the predominant magnetic fluctuations may differ significantly from those described by conventional spin fluctuation theory.

DOI
10.1073/pnas.2205048119

Related papers

Pairing glue in the two-dimensional Hubbard model

Emanuel Gull, Andrew J. Millis

Cluster dynamical mean-field calculations are used to construct the superconducting gap function of the two-dimensional Hubbard model. The frequency dependence of the imaginary part of the gap function indicates that the pairing is dominated by fluctuations at two characteristic frequencies: one at the scale of the hopping matrix element $t$ and one at a much lower scale. The lower-frequency component becomes more important as the doping is reduced into the pseudogap regime. Comparison to information on the spin-fluctuation spectrum of the model suggests that superconductivity arises from exchange of spin fluctuations. The inferred pairing glue function is in remarkable qualitative consistency with the pairing function inferred from optical conductivity data.

arXiv:1407.0704•Physical Review B•Jul 28, 2014•44 citations

Superconducting Phase and Pairing Fluctuations in the Half-Filled Two-Dimensional Hubbard Model

Michael A. Sentef, Philipp Werner, Emanuel Gull +1 more

The two-dimensional Hubbard model exhibits superconductivity with d-wave symmetry even at half-filling in the presence of a next-nearest neighbor hopping. Using plaquette cluster dynamical mean-field theory with a continuous-time quantum Monte Carlo impurity solver, we reveal the non-Fermi liquid character of the metallic phase in proximity to the superconducting state. Specifically, the low-frequency scattering rate for momenta near (π, 0) varies nonmonotonically at low temperatures, and the dc conductivity is T linear at elevated temperatures with an upturn upon cooling. Evidence is provided that pairing fluctuations dominate the normal-conducting state even considerably above the superconducting transition temperature.

arXiv:1102.1911•Physical Review Letters•Sep 14, 2011•40 citations

Interplay between the Pseudogap and Superconductivity in Doped Mott Insulators: a Cluster Dynamical Mean-Field Theory Study

Jinbin 晋斌 Liu 刘, Dao‐Xin Yao, Wéi Wú

Abstract We investigate the interplay between the pseudogap state and d-wave superconductivity in the two-dimensional doped Hubbard model by employing an eight-site cluster dynamical mean-field theory method. By tuning electron hopping parameters, the strong-coupling pseudogap in the two-dimensional Hubbard model can be either enhanced or suppressed in the doped Mott insulator regime. We find that in underdoped cases, the closing of pseudogap leads to a significant enhancement of superconductivity, indicating competition between the two in the underdoped regime. In contrast, at large dopings, suppressing the pseudogap is accompanied by a concurrent decrease in the superconducting transition temperature T c, which can be attributed to a reduction in antiferromagnetic correlations behind both the pseudogap and superconductivity. We elucidate this evolving relationship between pseudogap and superconductivity across different doping regimes.

Chinese Physics Letters•Jul 7, 2025•4 citations

Superconductivity in the two-dimensional Hubbard model with cellular dynamical mean-field theory: A quantum impurity model analysis

C. Walsh, M. Charlebois, P. Sémon +2 more

Doping a Mott insulator gives rise to unconventional superconducting correlations. Here we address the interplay between $d$-wave superconductivity and Mott physics using the two-dimensional Hubbard model with cellular dynamical mean-field theory on a $2\ifmmode\times\else\texttimes\fi{}2$ plaquette. Our approach is to study superconducting correlations from the perspective of a cluster quantum impurity model embedded in a self-consistent bath. At the level of the cluster, we calculate the probabilities of the possible cluster electrons configurations. Upon condensation, we find an increased probability that cluster electrons occupy a four-electron singlet configuration, enabling us to identify this type of short-range spin correlation as key to superconducting pairing. The increased probability of this four-electron singlet comes at the expense of a reduced probability of a four-electron triplet with no significant probability redistribution of fluctuations of charges. This allows us to establish that superconductivity at the level of the cluster primarily involves a reorganization of short-range spin correlations rather than charge correlations. We gain information about the bath by studying the spectral weight of the hybridization function. Upon condensation, we find a transfer of spectral weight leading to the opening of a superconducting gap. We use these insights to interpret the signatures of superconducting correlations in the density of states of the system and in the zero-frequency spin susceptibility.

arXiv:2307.02681•Physical review. B./Physical review. B•Aug 28, 2023•5 citations

Exactly solvable model of strongly correlated d -wave superconductivity

Malte Harland, Sergey Brener, Mikhail I. Katsnelson +1 more

We present an infinite-dimensional lattice of two-by-two plaquettes, the quadruple Bethe lattice, with Hubbard interaction and solve it exactly by means of the cluster dynamical mean-field theory. It exhibits a $d$-wave superconducting phase that is related to a highly degenerate point in the phase diagram of the isolated plaquette at that the ground states of the particle number sectors $N=2,\phantom{\rule{4pt}{0ex}}3,\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}4$ cross. The superconducting gap is formed by the renormalized lower Slater peak of the correlated, hole-doped Mott insulator. We engineer parts of the interaction and find that pair hoppings between $X/Y$ momenta are the main two-particle correlations of the superconducting phase. The suppression of the superconductivity is caused by the diminishing of pair hopping correlations in the overdoped regime and by the charge blocking in the underdoped one. The optimal doping is $\ensuremath{\sim}0.15$ at which the underlying normal state shows a Lifshitz transition. Tuning intra- and interplaquette hoppings allows to disentangle superconductivity from antiferromagnetism as the latter requires larger interplaquette hoppings. We expect our results to provide additional insight into the nature of the superconductivity in cuprates.

arXiv:1905.12610•Physical review. B./Physical review. B•Jan 15, 2020•12 citations

Dynamics of Superconducting Pairs in the Two-Dimensional Hubbard Model

G. Sordi, E. M. O’Callaghan, C. Walsh +3 more

The frequency structure of the superconducting correlations in cuprates gives insights on the pairing mechanism. Here we present an exhaustive study of this problem in the two-dimensional Hubbard model with cellular dynamical mean-field theory. To this end, we systematically quantify the dependence on doping δ and interaction strength U of the superconducting gap, of the frequency scales where d-wave pairing occurs, and of their relative contribution to pairing. For all values of U and δ, we find pair-forming processes confined to frequencies set by the superexchange interaction and followed by pair-breaking processes, ruling out both pair-forming and pair-breaking processes on the scale of U. This suggests that at high frequencies, the effect of U is eliminated by the d-wave paring, and that at small frequencies, U generates the superexchange interaction that leads to low-frequency pair-forming processes providing the net contribution to pairing.

arXiv:2512.01124•Physical Review Letters•May 18, 2026•0 citations
We study the fluctuations responsible for pairing in the d -wave superconducting state of the two-dimensional Hubbard model at intermediate coupling within a cluster dynamical mean-field theory with a numerically exact quantum impurity solver. By analyzing how momentum- and frequency-dependent fluctuations generate the d -wave superconducting state in different representations, we identify antiferromagnetic fluctuations as the pairing glue of superconductivity in both the underdoped and the overdoped regime. Nevertheless, in the intermediate coupling regime, the predominant magnetic fluctuations may differ significantly from those described by conventional spin fluctuation theory.
Cluster dynamical mean-field calculations are used to construct the superconducting gap function of the two-dimensional Hubbard model. The frequency dependence of the imaginary part of the gap function indicates that the pairing is dominated by fluctuations at two characteristic frequencies: one at the scale of the hopping matrix element ttt and one at a much lower scale. The lower-frequency component becomes more important as the doping is reduced into the pseudogap regime. Comparison to information on the spin-fluctuation spectrum of the model suggests that superconductivity arises from exchange of spin fluctuations. The inferred pairing glue function is in remarkable qualitative consistency with the pairing function inferred from optical conductivity data.
The two-dimensional Hubbard model exhibits superconductivity with d-wave symmetry even at half-filling in the presence of a next-nearest neighbor hopping. Using plaquette cluster dynamical mean-field theory with a continuous-time quantum Monte Carlo impurity solver, we reveal the non-Fermi liquid character of the metallic phase in proximity to the superconducting state. Specifically, the low-frequency scattering rate for momenta near (π, 0) varies nonmonotonically at low temperatures, and the dc conductivity is T linear at elevated temperatures with an upturn upon cooling. Evidence is provided that pairing fluctuations dominate the normal-conducting state even considerably above the superconducting transition temperature.
Abstract We investigate the interplay between the pseudogap state and d-wave superconductivity in the two-dimensional doped Hubbard model by employing an eight-site cluster dynamical mean-field theory method. By tuning electron hopping parameters, the strong-coupling pseudogap in the two-dimensional Hubbard model can be either enhanced or suppressed in the doped Mott insulator regime. We find that in underdoped cases, the closing of pseudogap leads to a significant enhancement of superconductivity, indicating competition between the two in the underdoped regime. In contrast, at large dopings, suppressing the pseudogap is accompanied by a concurrent decrease in the superconducting transition temperature T c, which can be attributed to a reduction in antiferromagnetic correlations behind both the pseudogap and superconductivity. We elucidate this evolving relationship between pseudogap and superconductivity across different doping regimes.
Doping a Mott insulator gives rise to unconventional superconducting correlations. Here we address the interplay between ddd-wave superconductivity and Mott physics using the two-dimensional Hubbard model with cellular dynamical mean-field theory on a $2\ifmmode\times\else\texttimes\fi{}2$ plaquette. Our approach is to study superconducting correlations from the perspective of a cluster quantum impurity model embedded in a self-consistent bath. At the level of the cluster, we calculate the probabilities of the possible cluster electrons configurations. Upon condensation, we find an increased probability that cluster electrons occupy a four-electron singlet configuration, enabling us to identify this type of short-range spin correlation as key to superconducting pairing. The increased probability of this four-electron singlet comes at the expense of a reduced probability of a four-electron triplet with no significant probability redistribution of fluctuations of charges. This allows us to establish that superconductivity at the level of the cluster primarily involves a reorganization of short-range spin correlations rather than charge correlations. We gain information about the bath by studying the spectral weight of the hybridization function. Upon condensation, we find a transfer of spectral weight leading to the opening of a superconducting gap. We use these insights to interpret the signatures of superconducting correlations in the density of states of the system and in the zero-frequency spin susceptibility.
We present an infinite-dimensional lattice of two-by-two plaquettes, the quadruple Bethe lattice, with Hubbard interaction and solve it exactly by means of the cluster dynamical mean-field theory. It exhibits a ddd-wave superconducting phase that is related to a highly degenerate point in the phase diagram of the isolated plaquette at that the ground states of the particle number sectors N=2,3,and4N=2,\phantom{\rule{4pt}{0ex}}3,\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}4N=2,3,and4 cross. The superconducting gap is formed by the renormalized lower Slater peak of the correlated, hole-doped Mott insulator. We engineer parts of the interaction and find that pair hoppings between X/YX/YX/Y momenta are the main two-particle correlations of the superconducting phase. The suppression of the superconductivity is caused by the diminishing of pair hopping correlations in the overdoped regime and by the charge blocking in the underdoped one. The optimal doping is $\ensuremath{\sim}0.15$ at which the underlying normal state shows a Lifshitz transition. Tuning intra- and interplaquette hoppings allows to disentangle superconductivity from antiferromagnetism as the latter requires larger interplaquette hoppings. We expect our results to provide additional insight into the nature of the superconductivity in cuprates.
The frequency structure of the superconducting correlations in cuprates gives insights on the pairing mechanism. Here we present an exhaustive study of this problem in the two-dimensional Hubbard model with cellular dynamical mean-field theory. To this end, we systematically quantify the dependence on doping δ and interaction strength U of the superconducting gap, of the frequency scales where d-wave pairing occurs, and of their relative contribution to pairing. For all values of U and δ, we find pair-forming processes confined to frequencies set by the superexchange interaction and followed by pair-breaking processes, ruling out both pair-forming and pair-breaking processes on the scale of U. This suggests that at high frequencies, the effect of U is eliminated by the d-wave paring, and that at small frequencies, U generates the superexchange interaction that leads to low-frequency pair-forming processes providing the net contribution to pairing.