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:cond-mat/0403403 · Physical Review B

Absence of the d -density-wave state from the two-dimensional Hubbard model

Alexandru Macridin, Mark Jarrell, Thomas Maier

Published Sep 24, 2004• 27 citations
arXivHTMLPDF

Abstract

Using the dynamical cluster approximation (DCA) we calculate the alternating circulating-current susceptibility and investigate the transition to the $d$-density wave (DDW) order in the two-dimensional Hubbard model. The $2\ifmmode\times\else\texttimes\fi{}2$ cluster used in the DCA calculation is the smallest that can capture $d$-wave order; therefore, due to the mean-field character of our calculation, we expect to overestimate the DDW transition temperatures. Despite this, we found no transition to the DDW state. On the other hand, DCA captures well the pseudogap features, showing that the pseudogap is not caused by the DDW order. In the pseudogap region the DDW susceptibility is enhanced, as predicted by the slave boson $SU(2)$ theory, but it still is much smaller than the $d$-wave pairing susceptibility.

DOI
10.1103/physrevb.70.113105

Related papers

Dynamical cluster approximation plus semiclassical approximation study for a Mott insulator and d-wave pairing

SungKun Kim, Hunpyo Lee

Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.

Journal of the Korean Physical Society•Jun 1, 2017•2 citations

Pseudogaps in the 2D Hubbard Model

Carey Huscroft, Mark Jarrell, Thomas Maier +2 more

We study the pseudogaps in the spectra of the 2D Hubbard model using both finite-size and dynamical cluster approximation (DCA) quantum Monte Carlo calculations. At half-filling, a charge pseudogap, accompanied by non-Fermi-liquid behavior in the self-energy, is shown to persist in the thermodynamic limit. The DCA (finite-size) method systematically underestimates (overestimates) the width of the pseudogap. A spin pseudogap is not seen at half-filling. At finite doping, a divergent d-wave pair susceptibility is observed.

Physical Review Letters•Jan 1, 2001•132 citations

Validity of the spin-susceptibility “glue” approximation for pairing in the two-dimensional Hubbard model

Ehsan Khatami, Alexandru Macridin, Mark Jarrell

We examine the validity of the weak-coupling spin-susceptibility ``glue'' approximation (SSGA) in a two-dimensional Hubbard model for cuprates. For comparison, we employ the well-established dynamical cluster approximation (DCA) with a quantum Monte Carlo algorithm as a cluster solver. We compare the leading eigenvalues and corresponding eigenfunctions of the DCA and SSGA pairing matrices. For realistic model parameters, we find that the SSGA fails to capture the leading pairing symmetries seen in the DCA. Furthermore, when the SSGA is improved through the addition of a term with $d$-wave symmetry, the strength of this additional term is found to be larger than that of the glue approximation.

arXiv:0901.4802•Physical Review B•Nov 25, 2009•4 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

Phase diagram of the Hubbard model: Beyond the dynamical mean field

Mark Jarrell, Thomas Maier, Matthias H. Hettler +1 more

The Dynamical Cluster Approximation (DCA) is used to study non-local corrections to the dynamical mean-field phase diagram of the two-dimensional Hubbard model. Regions of antiferromagnetic, d-wave superconducting, pseudo-gapped non-Fermi liquid, and Fermi liquid behaviors are found, in rough agreement with the generic phase diagram of the cuprates. The non-local fluctuations beyond the mean field both suppress the antiferromagnetism and mediate the superconductivity.

•Jan 1, 2007•36 citations

Phase diagram of the Hubbard model: Beyond the dynamical mean field

M Jarrell, Th Maier, M. H Hettler +1 more

The Dynamical Cluster Approximation (DCA) is used to study non-local corrections to the dynamical mean-field phase diagram of the two-dimensional Hubbard model. Regions of antiferromagnetic, d -wave superconducting, pseudo-gapped non-Fermi liquid, and Fermi liquid behaviors are found, in rough agreement with the generic phase diagram of the cuprates. The non-local fluctuations beyond the mean field both suppress the antiferromagnetism and mediate the superconductivity.

arXiv:cond-mat/0011282•Europhysics Letters (EPL)•Nov 1, 2001•77 citations
Using the dynamical cluster approximation (DCA) we calculate the alternating circulating-current susceptibility and investigate the transition to the ddd-density wave (DDW) order in the two-dimensional Hubbard model. The 2\ifmmode×\else\texttimes\fi22\ifmmode\times\else\texttimes\fi{}22\ifmmode×\else\texttimes\fi2 cluster used in the DCA calculation is the smallest that can capture ddd-wave order; therefore, due to the mean-field character of our calculation, we expect to overestimate the DDW transition temperatures. Despite this, we found no transition to the DDW state. On the other hand, DCA captures well the pseudogap features, showing that the pseudogap is not caused by the DDW order. In the pseudogap region the DDW susceptibility is enhanced, as predicted by the slave boson SU(2)SU(2)SU(2) theory, but it still is much smaller than the ddd-wave pairing susceptibility.
Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.
We study the pseudogaps in the spectra of the 2D Hubbard model using both finite-size and dynamical cluster approximation (DCA) quantum Monte Carlo calculations. At half-filling, a charge pseudogap, accompanied by non-Fermi-liquid behavior in the self-energy, is shown to persist in the thermodynamic limit. The DCA (finite-size) method systematically underestimates (overestimates) the width of the pseudogap. A spin pseudogap is not seen at half-filling. At finite doping, a divergent d-wave pair susceptibility is observed.
We examine the validity of the weak-coupling spin-susceptibility ``glue'' approximation (SSGA) in a two-dimensional Hubbard model for cuprates. For comparison, we employ the well-established dynamical cluster approximation (DCA) with a quantum Monte Carlo algorithm as a cluster solver. We compare the leading eigenvalues and corresponding eigenfunctions of the DCA and SSGA pairing matrices. For realistic model parameters, we find that the SSGA fails to capture the leading pairing symmetries seen in the DCA. Furthermore, when the SSGA is improved through the addition of a term with ddd-wave symmetry, the strength of this additional term is found to be larger than that of the glue approximation.
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.