Maier, Jarrell, and Pruschke Reply:

Abstract

Maier, Jarrell, and Pruschke Reply: In his Comment [1] on our letter [2] the author claims that our numerical results for the 2D Hubbard model contradict exact results published by the author. There, it was rigorously shown that the 2D Hubbard model does not exhibit d-wave pairing long-range order at finite temperatures. This result and the Mermin-Wagner theorem precludes long-range order with a broken continuous symmetry in two dimensions [3,4]. Although within our method we do find stable d-wave superconducting solutions in the 2D model, our results do not contradict this theorem.In our Letter we presented numerical results for the 2D Hubbard model obtained with the dynamical cluster approximation (DCA). The DCA systematically incorporates causal nonlocal corrections to the dynamical mean-field approximation (DMFA) by mapping the lattice system onto an embedded cluster of size N c . Our calculation explores the initial corrections to the mean-field superconducting phase diagram of the DMFA. We used the smallest cluster (N c 4) which allows for a d-wave transition and maintains the translational and point-group symmetries of the lattice. Therefore short-ranged interactions (of the order of the cluster size) are included accurately, whereas longer-ranged interactions are treated on a mean-field level within our approach.It is well known that such methods with mean-field character yield finite transition temperatures and second order transitions even for two dimensions. However, the mean-field character of the DCA can gradually be reduced as N C tends to infinity. The author of the Comment further objected to an alleged statement in our paper that the transition we observed was identified as Kosterlitz-Thouless transition. No such statement was made. Although we did speculate about the limit of large N c and cite other such speculations [5], we did not present any scaling calculations, and this was not the thrust of our paper. Indeed, N c 4 is the largest cluster that can be treated with noncrossing approximation calculations used to obtain the results presented in our paper.The mean-field character of our calculation can be stabilized as N c !`by introducing a coupling t Ќ [6] into the third dimension t Ќ ͑k x , k y , k z ͒ 22t Ќ ͑cosk x 2 cosk y ͒ 2 cosk z (1)

Finite-temperature phase diagram of nonmagnetic impurities in high-temperature superconductors using ad=3 tJmodel with quenched disorder

“…This reappearance of long-range AF order upon addition of impurities, at small hole dopings away from half filling where it does not exist in the pure case, was replicated in the d =2 tJ model using a self-consistent diagrammatic approach 34 and in the d =2 Hubbard model with the dynamical cluster approximation. 35 Thus the enhancement of the AF phase away from half filling, which we find at small impurity concentrations, is consistent with previous experimental and theoretical indications.…”

Nonadiabatic sudden increase of the cooperative kinetic effect at lattice energy stabilization—Microscopic mechanism of superconducting state transition: Model study of MgB2

“…In this case, nonzero contribution comes from interaction of unoccupied {B} states of the 1 band with occupied states {I} of the 2 (} band, the first term in Eq. (18). For quasicontinuum of states, with incorporation of the Lorenz line-shape form of the phonon mode, the correction reads…”

“…Some aspects of the d-wave superconductivity can be described within the models of strongly correlated electrons, e.g., Hubbard-like or t-J models (see, e.g., Refs. [17][18][19][20]), even without the explicit account for EP interactions. The competition between Coulomb vs. EP interactions has been intensively studied within the Holstein-Hubbard models [8,[21][22][23][24] with both interactions introduced in short-range order.…”

N‐bands Hubbard models. IV. Comparisons of electron‐ or hole‐doped quaternary oxypictides LaOMPn superconductors with cuprates

“…In this sense, quantitative theories of electron correlations developed in Figure 4 would be promising even in the intersection area of material science and quantum chemistry. Extensions of first principle nonperturbative methods [137][138][139][140][141][142] to strongly correlated systems are desirable for developments of microscopic theories to rationalize the phase diagrams in Figures 8 and 9. …”