The charge spin-separation, pseudogap formation and phase diagrams are studied in two and four site Hubbard clusters using analytical diagonalization and grand canonical ensemble method in a multidimensional parameter space of temperature, magnetic field, on-site Coulomb interaction (
U≥0), and chemical potential. The numerically evaluated, exact expressions for charge and spin susceptibilities provide clear evidence for the existence of true gaps in the ground state and pseudogaps in a limited range of temperature. In particular, Mott-Hubbard type charge crossover, spin pseudogap and magnetic correlations with antiferromagnetic (spin) pseudogap structure for two and four site clusters closely resemble the pseudogap phenomena and the normal-state phase diagram in high T
c superconductors. ~ ~
The phase diagram of hole-doped high-temperature superconductors remains puzzling. A state of matter with unusual physical properties, dubbed pseudogap, is found below a characteristic temperature
T∗ in a doped Mott insulator. Since the superconducting state is born out of the pseudogap over much of the phase diagram, the nature of the pseudogap is a fundamental issue in the field and it is under intense theoretical and experimental scrutiny. In many cases, it is not even clear whether
T∗ is a crossover or a phase transition. Here we show, by constructing the normal-state phase diagram of the archetypal model of strongly correlated electron systems, that
T∗ is a crossover line above a critical endpoint, while below that point it is a first-order phase transition between two metallic phases, one with a pseudogap and one without. Thus
T∗ appears in a new light: it is an unexpected example of a phenomenon observed in fluids, namely a sharp crossover between different dynamical regimes along a line of thermodynamic anomalies that appears above a first-order phase transition, the Widom line. Our findings thus suggest that the critical point of a first-order transition can be the organizing principle for the rich behavior of the normal state of the cuprates.
We present an effective Hamiltonian based real-space approach for studying the weak-coupling BCS to the strong-coupling Bose-Einstein condensate crossover in the two-dimensional attractive Hubbard model at finite temperatures. We introduce and justify an effective classical Hamiltonian to describe the thermal fluctuations of the relevant auxiliary fields. Our results for
Tc and phase diagrams compare very well with those obtained from more sophisticated and CPU-intensive numerical methods. We demonstrate that the method works in the presence of disorder and can be a powerful tool for a real-space description of the effect of disorder on superconductivity. From a combined analysis of the superconducting order parameter, the distribution of auxiliary fields, and the quasiparticle density of states, we identify the regions of metallic, insulating, superconducting, and pseudogapped behavior. Our finding of the importance of phase fluctuations for the pseudogap behavior is consistent with the conclusions drawn from recent experiments on NbN superconductors. The method can be generalized to study superconductors with nontrivial order-parameter symmetries by identifying the relevant auxiliary variables.