We have made a variational analysis on an evolution of superconductivity from weak to strong coupling regime. In contrast to a crossover without thermodynamic anomaly found in a dilute system, we show the existence of a quantum phase transition near half filling. The transition is driven by charge density waves instabilities. We have found that superconductivity and charge density waves coexist in the presence of a weak intersite repulsion. The ground state phase diagram is determined and the quantum phase transition is an attractive version of the Mott transition.
We discuss the density-density response functions and the collective excitation spectrum for the extended Hubbard model with on-site attraction and arbitrary electron density, in the superconducting ground state.For the short-range intersite interaction we find the sound wave-like modes with the velocity interpolating smoothly between the weak (v 2Zt, |UD <2Zt) and strong coupling (v > 2Zt) limits.The latter agrees with the results obtained from an effective pseudospin Hamiltonian valid in the strong coupling limit.In the weak coupling regime, we obtain that apart from a commensurate charge density wave instability, an increase in the intersite Coułomb repulsion can give rise to a charge density wave incommensurate with the lattice period, away from half-frlling.The ground state phase diagram for 2D square lattice, including singlet superconducting ground state, electronic droplet formation, and charge density waves is determined.It is also shown that the energy of collective excitations evolves smoothly from weak to strong coupling limit for a 2D lattice, in the case of a long-range Coulomb interaction.Finally, the mode coupling effects in the frequency behavior of the density-density response functions are analyzed.
We provide a quantitative and controlled analysis of the phase diagram of the Yukawa-Sachdev-Ye-Kitaev model on a lattice, in the normal and superconducting states. We analyze the entire crossover from Bardeen-Cooper-Schrieffer (BCS)/weak coupling to Eliashberg/strong coupling superconductivity, as a function of fermion-boson interaction strength and hopping parameter. Cooper pairs of sharp Fermi-liquid quasiparticles at weak coupling evolve into pairing of fully incoherent fermions in the non-Fermi liquid regime. The crossovers leave observable traces in the critical temperature, the zero-temperature and zero-energy gap, the entropy, and the phase stiffness.
By using variational wave functions and quantum Monte Carlo techniques, we investigate the interplay between electron-electron and electron-phonon interactions in the two-dimensional Hubbard-Holstein model. Here, the ground-state phase diagram is triggered by several energy scales, i.e., the electron hopping
t, the on-site electron-electron interaction
U, the phonon energy ${\ensuremath{\omega}}_{0}$, and the electron-phonon coupling
g. At half filling, the ground state is an antiferromagnetic insulator for $U\ensuremath{\gtrsim}2{g}^{2}/{\ensuremath{\omega}}_{0}$, while it is a charge-density-wave (or bipolaronic) insulator for $U\ensuremath{\lesssim}2{g}^{2}/{\ensuremath{\omega}}_{0}$. In addition to these phases, we find a superconducting phase that intrudes between them. For ${\ensuremath{\omega}}_{0}/t=1$, superconductivity emerges when both
U/t and $2{g}^{2}/t{\ensuremath{\omega}}_{0}$ are small; then, by increasing the value of the phonon energy ${\ensuremath{\omega}}_{0}$, it extends along the transition line between antiferromagnetic and charge-density-wave insulators. Away from half filling, phase separation occurs when doping the charge-density-wave insulator, while a uniform (superconducting) ground state is found when doping the superconducting phase. In the analysis of finite-size effects, it is extremely important to average over twisted boundary conditions, especially in the weak-coupling limit and in the doped case.
We study the collective excitations of a system with local attractive interactions as a function of the coupling strength. The two-particle excitations are obtained in the random-phase approximation. For the strong-coupling limit we reproduce the excitation spectrum of a hard-core Bose gas, while in the weak-coupling limit we obtained a spectrum consistent with the BCS picture. The evolution of the excitation spectrum from the weak- to the strong-coupling limits is continuous. We briefly discuss the effect of these excitations in the thermodynamic properties of the system.
Cooperation and competition between the antiferromagnetic,
d-wave superconducting, and Mott-insulating states are explored for the two-dimensional Hubbard model including nearest and next-nearest-neighbor hoppings at zero temperature. Using the variational cluster approach with clusters of different shapes and sizes up to 10 sites, it is found that the doping-driven transition from a phase with microscopic coexistence of antiferromagnetism and superconductivity to a purely superconducting phase is discontinuous for strong interaction and accompanied by phase separation. At half-filling the system is in an antiferromagnetic Mott-insulating state with vanishing charge compressibility. Upon decreasing the interaction strength
U below a certain critical value of roughly ${U}_{c}\ensuremath{\sim}4$ (in units of the nearest-neighbor hopping), however, the filling-dependent magnetic transition changes its character and becomes continuous. Phase separation or, more carefully, the tendency towards the formation of inhomogeneous states disappears. This critical value is in contrast to previous studies, where a much larger value was obtained. Moreover, we find that the system at half-filling undergoes the Mott transition from an insulator to a state with a finite charge compressibility at essentially the same value. The weakly correlated state at half-filling exhibits superconductivity microscopically admixed to the antiferromagnetic order. This scenario suggests a close relation between phase separation and the Mott-insulator physics.