The properties of a phase with large correlation length can be strongly influenced by the underlying normal phase. We illustrate this by studying the half-filled two-dimensional Hubbard model using cellular dynamical mean-field theory with continuous-time quantum Monte Carlo. Sharp crossovers in the mechanism that favors antiferromagnetic correlations and in the corresponding local density of states are observed. These crossovers occur at values of the interaction strength U and temperature T that are controlled by the underlying normal-state Mott transition.

Since its experimental discovery, many phenomenological theories successfully reproduced the rapid rise of the Hall number nH , going from p at low doping to 1 + p at the critical doping p * of the pseudogap in superconducting cuprates. Further comparison with experiments is now needed in order to narrow down candidates. In this paper, we consider three previously successful phenomenological theories in a unified formalism-an antiferromagnetic mean field (AF), a spiral incommensurate antiferromagnetic mean field (sAF), and the Yang-Rice-Zhang (YRZ) theory. We find a rapid rise in the specific heat and a rapid drop in the Seebeck coefficient for increasing doping across the transition in each of those models. The predicted rises and drops are locked, not to p * , but to the doping where anti-nodal electron pockets, characteristic of each model, appear at the Fermi surface shortly before p * . While such electron pockets are still to be found in experiments, we discuss how they could provide distinctive signatures for each model. We also show that the range of doping where those electron pockets would be found is strongly affected by the position of the van Hove singularity.

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The nearest-neighbor superexchange-mediated mechanism for d x 2 −y 2 superconductivity in the one-band Hubbard model faces the challenge that nearest-neighbor Coulomb repulsion can be larger than superexchange. To answer this question, we use cellular dynamical mean-field theory (CDMFT) with a continuous-time quantum Monte Carlo solver to determine the superconducting phase diagram as a function of temperature and doping for on-site repulsion U = 9t and nearest-neighbor repulsion V = 0, 2t, 4t. In the underdoped regime, V increases the CDMFT superconducting transition temperature T d c even though it decreases the superconducting order parameter at low temperature for all dopings. However, in the overdoped regime V decreases T d c . We gain insight into these paradoxical results through a detailed study of the frequency dependence of the anomalous spectral function, extracted at finite temperature via the MaxEntAux method for analytic continuation. A systematic study of dynamical positive and negative contributions to pairing reveals that even though V has a high-frequency depairing contribution, it also has a low frequency pairing contribution since it can reinforce superexchange through J = 4t 2 /(U − V ). Retardation is thus crucial to understand pairing in doped Mott insulators, as suggested by previous zero-temperature studies. We also comment on the tendency to charge order for large V and on the persistence of d-wave superconductivity over extended-s or s + d-wave.