Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models

The Luttinger-Ward functional $\Phi[\mathbf{G}]$, which expresses the thermodynamic grand potential in terms of the interacting single-particle Green's function $\mathbf{G}$, is found to be ill-defined for fermionic models with the Hubbard on-site interaction. In particular, we show that the self-energy $\mathbf{\Sigma}[\mathbf{G}] \propto \delta\Phi[\mathbf{G}]/\delta \mathbf{G}$ is not a single-valued functional of $\mathbf{G}$: in addition to the physical solution for $\mathbf{\Sigma}[\mathbf{G}]$, there exists at least one qualitatively distinct unphysical branch. This result is demonstrated for several models: the Hubbard atom, the Anderson impurity model, and the full two-dimensional Hubbard model. Despite this pathology, the skeleton Feynman diagrammatic series for $\mathbf{\Sigma}$ in terms of $\mathbf{G}$ is found to converge at least for moderately low temperatures. However, at strong interactions, its convergence is to the unphysical branch. This reveals a new scenario of breaking down of diagrammatic expansions. In contrast, the bare series in terms of the non-interacting Green's function $\mathbf{G}_0$ converges to the correct physical branch of $\mathbf{\Sigma}$ in all cases currently accessible by diagrammatic Monte Carlo. Besides their conceptual importance, these observations have important implications for techniques based on the explicit summation of diagrammatic series.Comment: 5 pages, 5 figure

Orbital Polarization in Strained LaNiO3_{3}: Structural Distortions and Correlation Effects

Transition-metal heterostructures offer the fascinating possibility of controlling orbital degrees of freedom via strain. Here, we investigate theoretically the degree of orbital polarization that can be induced by epitaxial strain in LaNiO$_3$ films. Using combined electronic structure and dynamical mean-field theory methods we take into account both structural distortions and electron correlations and discuss their relative influence. We confirm that Hund's rule coupling tends to decrease the polarization and point out that this applies to both the $d^8\underline{L}$ and $d^7$ local configurations of the Ni ions. Our calculations are in good agreement with recent experiments, which revealed sizable orbital polarization under tensile strain. We discuss why full orbital polarization is hard to achieve in this specific system and emphasize the general limitations that must be overcome to achieve this goal.Comment: 13 pages, 13 figure

Dynamical behavior across the Mott transition of two bands with different bandwidths

We investigate the role of the bandwidth difference in the Mott metal-insulator transition of a two-band Hubbard model in the limit of infinite dimensions, by means of a Gutzwiller variational wave function as well as by dynamical mean-field theory. The variational calculation predicts a two-stage quenching of the charge degrees of freedom, in which the narrower band undergoes a Mott transition before the wider one, both in the presence and in the absence of a Hund's exchange coupling. However, this scenario is not fully confirmed by the dynamical mean-field theory calculation, which shows that, although the quasiparticle residue of the narrower band is zero within our numerical accuracy, low-energy spectral weight still exists inside the Mott-Hubbard gap, concentrated into two peaks symmetric around the chemical potential. This spectral weight vanishes only when the wider band ceases to conduct too. Although our results are compatible with several scenarios, e.g., a narrow gap semiconductor or a semimetal, we argue that the most plausible one is that the two peaks coexist with a narrow resonance tied at the chemical potential, with a spectral weight below our numerical accuracy. This quasiparticle resonance is expected to vanish when the wider band undergoes the Mott transition.Comment: 11 pages, 12 figure

TRIQS/CTHYB: A Continuous-Time Quantum Monte Carlo Hybridization Expansion Solver for Quantum Impurity Problems

We present TRIQS/CTHYB, a state-of-the art open-source implementation of the continuous-time hybridisation expansion quantum impurity solver of the TRIQS package. This code is mainly designed to be used with the TRIQS library in order to solve the self-consistent quantum impurity problem in a multi-orbital dynamical mean field theory approach to strongly-correlated electrons, in particular in the context of realistic calculations. It is implemented in C++ for efficiency and is provided with a high-level Python interface. The code is ships with a new partitioning algorithm that divides the local Hilbert space without any user knowledge of the symmetries and quantum numbers of the Hamiltonian. Furthermore, we implement higher-order configuration moves and show that such moves are necessary to ensure ergodicity of the Monte Carlo in common Hamiltonians even without symmetry-breaking.Comment: 19 pages, this is a companion article to that describing the TRIQS librar

Theoretical prediction and spectroscopic fingerprints of an orbital transition in CeCu2Si2

We show that the heavy-fermion compound CeCu2Si2 undergoes a transition between two regimes dominated by different crystal-field states. At low pressure P and low temperature T the Ce 4f electron resides in the atomic crystal-field ground state, while at high P or T the electron occupancy and spectral weight is transferred to an excited crystal-field level that hybridizes more strongly with itinerant states. These findings result from first-principles dynamical-mean-field-theory calculations. We predict experimental signatures of this orbital transition in X-ray spectroscopy. The corresponding fluctuations may be responsible for the second high-pressure superconducting dome observed in this and similar materials.Comment: 5 pages, 4 figures + 5 supplementary page

Simple predictors of TcT_c in superconducting cuprates reveal role of interactions between effective Wannier orbitals in the d−pd-p 3-band model

At optimal doping, different cuprate compounds can exhibit vastly different critical temperatures for superconductivity ($T_c$), ranging from about 20 K to about 135 K. The precise properties of the lattice that determine the magnitude of the $T_c$ are currently unknown. In this paper, we investigate the dependence of the optimal doping $T_c$ on the parameters of the Emery ($d-p$) model for the CuO$_2$ planes in the cuprates. We show that the best scaling is obtained not with the parameters of the model written in the real ($d/p$-orbital) space, but rather written in the space of effective Wannier orbitals. In this basis, one obtains a model of three sublattices coupled through all possible 4-point interactions. We identify multiple predictor variables that fit the experimental $T_c$ to about $\pm4$ K and that depend on the coupling constants in the transformed Hamiltonian.Comment: 6 pages, 2 figures + supp. mat. 15 pages, 10 figure

How bad metals turn good: spectroscopic signatures of resilient quasiparticles

We investigate transport in strongly correlated metals. Within dynamical mean-field theory, we calculate the resistivity, thermopower, optical conductivity and thermodynamic properties of a hole-doped Mott insulator. Two well-separated temperature scales are identified: T_FL below which Landau Fermi liquid behavior applies, and T_MIR above which the resistivity exceeds the Mott-Ioffe-Regel value and `bad-metal' behavior is found. We show that quasiparticle excitations remain well-defined above T_FL and dominate transport throughout the intermediate regime T_FL < T_MIR. The lifetime of these `resilient quasiparticles' is longer for electron-like excitations, and this pronounced particle-hole asymmetry has important consequences for the thermopower. The crossover into the bad-metal regime corresponds to the disappearance of these excitations, and has clear signatures in optical spectroscopy.Comment: 5 pages + 4 supplementary pages; published versio

Dynamics of the quantum dimer model on the triangular lattice: Soft modes and local resonating valence-bond correlations

We report on an exhaustive investigation of the dynamical dimer-dimer correlations in imaginary time for the quantum dimer model on the triangular lattice using the Green's function Monte Carlo method. We show in particular that soft modes develop upon reducing the dimer-dimer repulsion, indicating the presence of a second-order phase transition into an ordered phase with broken translational symmetry. We further investigate the nature of this ordered phase, for which a 12-site unit cell has been previously proposed, with the surprising result that significant Bragg peaks are only present at two of the three high-symmetry points consistent with this unit cell. We attribute the absence of a detectable peak to its small magnitude due to the nearly uniform internal structure of the 12-site crystal cell.Comment: 6 pages, 8 figure