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AIP conference proceedings

Study of d- and p-wave Pairing in the Hubbard Model Using the Dynamical Cluster Approximation

Ryotaro Arita, Karsten Held

Published Jan 1, 2006• 0 citations
Publisher

Abstract

The Hubbard model is commonly considered to be relevant for unconventional superconductors like cuprates and ruthenates. For a more thorough insight into the physics of this model, we use a new projective quantum Monte Carlo (PQMC) algorithm within the framework of the dynamical cluster approximation (DCA). Employing this DCA(PQMC) approach, we calculate static pairing susceptibilities for various symmetries and study the crossover from dx2−y2‐wave to px+y‐wave pairing as a function of doping.

DOI
10.1063/1.2354832

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The Hubbard model is commonly considered to be relevant for unconventional superconductors like cuprates and ruthenates. For a more thorough insight into the physics of this model, we use a new projective quantum Monte Carlo (PQMC) algorithm within the framework of the dynamical cluster approximation (DCA). Employing this DCA(PQMC) approach, we calculate static pairing susceptibilities for various symmetries and study the crossover from dx2−y2‐wave to px+y‐wave pairing as a function of doping.
We develop an algorithm which employs the projective quantum Monte Carlo method for solving the equations of the dynamical cluster approximation at zero temperature, and apply it for studying pair susceptibilities of the two-dimensional Hubbard-model with next-nearest neighbor hopping. In particular, we identify which pairing symmetry is dominant in the $U\ensuremath{-}n$ parameter space (UUU: repulsive Coulomb interaction; nnn: electron density). We find that ${p}_{x+{y}^{\ensuremath{-}}}({d}_{{x}^{2}\ensuremath{-}{y}^{2\ensuremath{-}}})$ wave is dominant among triplet (singlet) pairings---at least for 0.3<n<0.80.3<n<0.80.3<n<0.8 and $U\ensuremath{\leqslant}4t$. The crossover between ${d}_{{x}^{2}\ensuremath{-}{y}^{2\ensuremath{-}}}$ wave and ${p}_{x+{y}^{\ensuremath{-}}}$ wave occurs around $n\ensuremath{\sim}0.4$.
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.
We study the three-band Hubbard model for the copper oxide plane of the high-temperature superconducting cuprates using determinant quantum Monte Carlo and the dynamical cluster approximation (DCA) and provide a comprehensive view of the pairing correlations in this model using these methods. Specifically, we compute the pair-field susceptibility and study its dependence on temperature, doping, interaction strength, and charge-transfer energy. Using the DCA, we also solve the Bethe-Salpeter equation for the two-particle Green's function in the particle-particle channel to determine the transition temperature to the superconducting phase on smaller clusters. Our calculations reproduce many aspects of the cuprate phase diagram and indicate that there is an ``optimal'' value of the charge-transfer energy for the model where Tc{T}_{c}Tc​ is largest. These results have implications for our understanding of superconductivity in both the cuprates and other doped charge-transfer insulators.
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.
A dynamic cluster quantum Monte Carlo algorithm is used to study a spin-susceptibility representation of the pairing interaction for the two-dimensional Hubbard model with an on-site Coulomb interaction equal to the bandwidth for various doping levels. We find that the pairing interaction is well approximated by $\frac{3}{2}\overline{U}{(T)}^{2}\ensuremath{\chi}(K\ensuremath{-}{K}^{\ensuremath{'}})$, with an effective temperature and doping dependent coupling U‾(T)\overline{U}(T)U(T) and the numerically calculated spin susceptibility $\ensuremath{\chi}(K\ensuremath{-}{K}^{\ensuremath{'}})$. We show that at low temperatures, U‾\overline{U}U may be accurately determined from a corresponding spin-susceptibility based calculation of the single-particle self-energy. We conclude that the strength of the ddd-wave pairing interaction, characterized by the mean-field transition temperature, can be determined from a knowledge of the dressed spin susceptibility and the nodal quasiparticle spectral weight. This has important implications with respect to the questions of whether spin fluctuations are responsible for pairing in the high-Tc{T}_{c}Tc​ cuprates.
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.