We study the competition of antiferromagnetism and
d-wave superconductivity at zero temperature in the two-dimensional Hubbard model using cellular dynamical mean-field theory for a $2\ifmmode\times\else\texttimes\fi{}2$ plaquette, and solve the associated cluster impurity model at zero temperature by means of exact diagonalization. The interplay between the two phases depends strongly on the strength of the correlation. At strong coupling $(U\ensuremath{\gtrsim}8t)$ the two phases do not mix, and a first-order transition takes place as a function of doping between two pure phases. At weak coupling $(U\ensuremath{\lesssim}8t)$ the two order parameters coexist within the same solution in a range of doping and the system smoothly evolves from the antiferromagnet to the superconductor. When the transition between the superconducting and the antiferromagetic phases is of the first-order, it is accompanied by a phase separation.
Proximity to a Mott insulating phase is likely to be an important physical ingredient of a theory that aims to describe high-temperature superconductivity in the cuprates. Quantum cluster methods are well suited to describe the Mott phase. Hence, as a step toward a quantitative theory of the competition between antiferromagnetism and
d-wave superconductivity in the cuprates, we use cellular dynamical mean-field theory to compute zero-temperature properties of the two-dimensional square lattice Hubbard model. The
d-wave order parameter is found to scale like the superexchange coupling
J for on-site interaction
U comparable to or larger than the bandwidth. The order parameter also assumes a dome shape as a function of doping, while, by contrast, the gap in the single-particle density of states decreases monotonically with increasing doping. In the presence of a finite second neighbor hopping ${t}^{\ensuremath{'}}$, the zero-temperature phase diagram displays the electron-hole asymmetric competition between antiferromagnetism and superconductivity that is observed experimentally in the cuprates. Adding realistic third neighbor hopping ${t}^{\ensuremath{''}}$ improves the overall agreement with the experimental phase diagram. Since band parameters can vary depending on the specific cuprate considered, the sensitivity of the theoretical phase diagram to band parameters challenges the commonly held assumption that the doping vs
Tc∕Tcmax phase diagram of the cuprates is universal. The calculated angle-resolved photoemission spectrum displays the observed electron-hole asymmetry. The tendency to homogeneous coexistence of the superconducting and antiferromagnetic order parameters is stronger than observed in most experiments but consistent with many theoretical results and with experiments in some layered high-temperature superconductors. Clearly, our calculations reproduce important features of
d-wave superconductivity in the cuprates that would otherwise be considered anomalous from the point of view of the standard Bardeen--Cooper--Schrieffer approach. At strong coupling,
d-wave superconductivity and antiferromagnetism naturally appear as two equally important competing instabilities of the normal phase of the same underlying Hamiltonian.
We present the results of numerical studies of superconductivity and antiferromagnetism in a strongly correlated electron system. To do this we construct a Hubbard model on a lattice of self-consistently embedded multi-site clusters by means of a dynamical mean-field theory in which intra-cluster dynamics is treated essentially exactly. We show that a class of characteristic features which have been seen in the excitation spectra of high-
Tc cuprates (e.g., pseudogap and the spin-flip resonance), as well as their interplay with the onset of a pairing correlations, can be captured within a dynamical mean-field theory in which short-wavelength dynamics are rigorously treated. Thus we infer that the observation of the neutron scattering resonance in the superconducting state of the cuprate superconductors does not appear to be directly tied to their quasi-2D character. Although our approach is defined strictly in terms of fermion degrees of freedom, we show that we can readily identify the emergence of effective low energy bosonic degrees of freedom in the presence of a well-defined broken symmetry phase as long as their dynamics are dominated by short-range, short-wavelength fluctuations. Our results reveal that the dynamics of staggered spin degrees of freedom builds up coherence and a resonance-like sharp feature emerges as pairing correlations set in. Under conditions of superconducting broken symmetry our approach thus extends static BCS mean field theory to provide an exact treatment of quantum fluctuations of the BCS order parameter.
The interplay between antiferromagnetism and d-wave superconductivity is studied in a mean-field approximation for a generic microscopic Hamiltonian with short-range repulsion and near-neighbor attraction. In the presence of competing microscopic interactions, the phase boundaries of antiferromagnetic and superconducting states are significantly modified in some region of the doping-temperature plane. The transition between superconductivity and antiferromagnetism occurs through a phase where both order parameters coexist with a third, dynamically generated, spin-triplet amplitude. This dynamical generation of a new order parameter is not restricted to a system with antiferromagnetism and d-wave superconductivity, but is a generic feature for fermionic systems. The dynamically generated spin-triplet order parameter is found to be robust to variations in the mean-field Hamiltonian.