Benchmark of a modified Iterated Perturbation Theory approach on the 3d FCC lattice at strong coupling

The Dynamical Mean-Field theory (DMFT) approach to the Hubbard model requires a method to solve the problem of a quantum impurity in a bath of non-interacting electrons. Iterated Perturbation Theory (IPT) has proven its effectiveness as a solver in many cases of interest. Based on general principles and on comparisons with an essentially exact Continuous-Time Quantum Monte Carlo (CTQMC) solver, here we show that the standard implementation of IPT fails away from half-filling when the interaction strength is much larger than the bandwidth. We propose a slight modification to the IPT algorithm that replaces one of the equations by the requirement that double occupancy calculated with IPT gives the correct value. We call this method IPT-$D$. We recover the Fermi liquid ground state away from half-filling. The Fermi liquid parameters, density of states, chemical potential, energy and specific heat on the FCC lattice are calculated with both IPT-$D$ and CTQMC as benchmark examples. We also calculated the resistivity and the optical conductivity within IPT-$D$. Particle-hole asymmetry persists even at coupling twice the bandwidth. Several algorithms that speed up the calculations are described in appendices.Comment: 17 pages, 15 figures, minor changes to improve clarit

Importance of subleading corrections for the Mott critical point

The interaction-induced metal-insulator transition should be in the Ising universality class. Experiments on layered organic superconductors suggest that the observed critical endpoint of the first-order Mott transition belongs instead to a different universality class. To address this question, we use dynamical mean-field theory and a cluster generalization that is necessary to account for short-range spatial correlations in two dimensions. Such calculations can give information on crossover effects, in particular quantum ones, that are not included in the simplest mean-field. In the cluster calculation, a canonical transformation that minimizes the sign problem in continuous-time quantum Monte Carlo calculations allows us to obtain very accurate results for double occupancy. These results show that there are important subleading corrections that can lead to apparent exponents that are different from mean-field. Experiments on optical lattices could verify our predictions.Comment: 5 pages, 3 figures, late

Superconductivity in the two-dimensional Hubbard model with cellular dynamical mean-field theory: a quantum impurity model analysis

Doping a Mott insulator gives rise to unconventional superconducting correlations. Here we address the interplay between d-wave superconductivity and Mott physics using the two-dimensional Hubbard model with cellular dynamical mean-field theory on a $2\times2$ plaquette. Our approach is to study superconducting correlations from the perspective of a cluster quantum impurity model embedded in a self-consistent bath. At the level of the cluster, we calculate the probabilities of the possible cluster electrons configurations. Upon condensation we find an increased probability that cluster electrons occupy a four-electron singlet configuration, enabling us to identify this type of short-range spin correlations as key to superconducting pairing. The increased probability of this four-electron singlet comes at the expense of a reduced probability of a four-electron triplet with no significant probability redistribution of fluctuations of charges. This allows us to establish that superconductivity at the level of the cluster primarily involves a reorganisation of short-range spin correlations rather than charge correlations. We gain information about the bath by studying the spectral weight of the hybridization function. Upon condensation, we find a transfer of spectral weight leading to the opening of a superconducting gap. We use these insights to interpret the signatures of superconducting correlations in the density of states of the system and in the zero-frequency spin susceptibility.Comment: 19 pages, 10 figures; accepted versio