Mott physics and spin fluctuations: a unified framework

We present a formalism for strongly correlated electrons systems which consists in a local approximation of the dynamical three-leg interaction vertex. This vertex is self-consistently computed with a quantum impurity model with dynamical interactions in the charge and spin channels, similar to dynamical mean field theory (DMFT) approaches. The electronic self-energy and the polarization are both frequency and momentum dependent. The method interpolates between the spin-fluctuation or GW approximations at weak coupling and the atomic limit at strong coupling. We apply the formalism to the Hubbard model on a two-dimensional square lattice and show that as interactions are increased towards the Mott insulating state, the local vertex acquires a strong frequency dependence, driving the system to a Mott transition, while at low enough temperatures the momentum-dependence of the self-energy is enhanced due to large spin fluctuations. Upon doping, we find a Fermi arc in the one-particle spectral function, which is one signature of the pseudo-gap state.Comment: 7 pages, 6 figure

Mott physics and spin fluctuations: a functional viewpoint

We present a formalism for strongly correlated systems with fermions coupled to bosonic modes. We construct the three-particle irreducible functional $\mathcal{K}$ by successive Legendre transformations of the free energy of the system. We derive a closed set of equations for the fermionic and bosonic self-energies for a given $\mathcal{K}$. We then introduce a local approximation for $\mathcal{K}$, which extends the idea of dynamical mean field theory (DMFT) approaches from two- to three-particle irreducibility. This approximation entails the locality of the three-leg electron-boson vertex $\Lambda(i\omega,i\Omega)$, which is self-consistently computed using a quantum impurity model with dynamical charge and spin interactions. This local vertex is used to construct frequency- and momentum-dependent electronic self-energies and polarizations. By construction, the method interpolates between the spin-fluctuation or GW approximations at weak coupling and the atomic limit at strong coupling. We apply it to the Hubbard model on two-dimensional square and triangular lattices. We complement the results of Phys.Rev. B 92, 115109 by (i) showing that, at half-filling, as DMFT, the method describes the Fermi-liquid metallic state and the Mott insulator, separated by a first-order interacting-driven Mott transition at low temperatures, (ii) investigating the influence of frustration and (iii) discussing the influence of the bosonic decoupling channel.Comment: 29 pages, 14 figure

Enhancement of Local Pairing Correlations in Periodically Driven Mott Insulators

We investigate a model for a Mott insulator in presence of a time-periodic modulated interaction and a coupling to a thermal reservoir. The combination of drive and dissipation leads to non-equilibrium steady states with a large number of doublon excitations, well above the maximum thermal-equilibrium value. We interpret this effect as an enhancement of local pairing correlations, providing analytical arguments based on a Floquet Hamiltonian. Remarkably, this Hamiltonian shows a tendency to develop long-range staggered superconducting correlations. This suggests the possibility of realizing the elusive eta-pairing phase in driven-dissipative Mott Insulators.Comment: 6+5 page

Continuous-time auxiliary field Monte Carlo for quantum impurity models

We present a continuous-time Monte Carlo method for quantum impurity models, which combines a weak-coupling expansion with an auxiliary-field decomposition. The method is considerably more efficient than Hirsch-Fye and free of time discretization errors, and is particularly useful as impurity solver in large cluster dynamical mean field theory (DMFT) calculations.Comment: 6 pages, 5 figure

Mott physics and collective modes: an atomic approximation of the four-particle irreducible functional

14 pages, 6 figuresWe discuss a generalization of the dynamical mean field theory (DMFT) for strongly correlated systems close to a Mott transition based on a systematic approximation of the fully irreducible four-point vertex. It is an atomic-limit approximation of a functional of the one- and two-particle Green functions, built with the second Legendre transform of the free energy with respect to the two-particle Green function. This functional is represented diagrammatically by four-particle irreducible (4PI) diagrams. Like the dynamical vertex approximation (D$\Gamma$A), the fully irreducible vertex is computed from a quantum impurity model whose bath is self-consistently determined by solving the parquet equations. However, in contrast with D$\Gamma$A and DMFT, the interaction term of the impurity model is also self-consistently determined. The method interpolates between the parquet approximation at weak coupling and the atomic limit, where it is exact. It is applicable to systems with short-range and long-range interactions

Reconstructing non-equilibrium regimes of quantum many-body systems from the analytical structure of perturbative expansions

We propose a systematic approach to the non-equilibrium dynamics of strongly interacting many-body quantum systems, building upon the standard perturbative expansion in the Coulomb interaction. High order series are derived from the Keldysh version of determinantal diagrammatic Quantum Monte Carlo, and the reconstruction beyond the weak coupling regime of physical quantities is obtained by considering them as analytic functions of a complex-valued interaction $U$. Our advances rely on two crucial ingredients: i) a conformal change of variable, based on the approximate location of the singularities of these functions in the complex $U$-plane; ii) a Bayesian inference technique, that takes into account additional known non-perturbative relations, in order to control the amplification of noise occurring at large $U$. This general methodology is applied to the strongly correlated Anderson quantum impurity model, and is thoroughly tested both in- and out-of-equilibrium. In the situation of a finite voltage bias, our method is able to extend previous studies, by bridging with the regime of unitary conductance, and by dealing with energy offsets from particle-hole symmetry. We also confirm the existence of a voltage splitting of the impurity density of states, and find that it is tied to a non-trivial behavior of the non-equilibrium distribution function. Beyond impurity problems, our approach could be directly applied to Hubbard-like models, as well as other types of expansions.Comment: 16 pages, 18 figures, added comparison with Bethe Ansatz, appendix B and some discussio

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

Hall coefficient signals orbital differentiation in the Hund's metal Sr2_2RuO4_4

The Hall coefficient $R_H$ of Sr$_2$RuO$_4$ exhibits a non-monotonic temperature dependence with two sign reversals. We show that this puzzling behavior is the signature of two crossovers which are key to the physics of this material. The increase of $R_H$ and the first sign change upon cooling are associated with a crossover into a regime of coherent quasiparticles with strong orbital differentiation of the inelastic scattering rates. The eventual decrease and the second sign change at lower temperature is driven by the crossover from inelastic to impurity-dominated scattering. This qualitative picture is supported by quantitative calculations of $R_H(T)$ using Boltzmann transport theory in combination with dynamical mean-field theory, taking into account the effect of spin-orbit coupling. Our insights shed new light on the temperature dependence of the Hall coefficient in materials with strong orbital differentiation, as observed in Hund's metals.Comment: 20 pages, 4 figure

Conserving many body approach to the fully screened, infinite U Anderson model

Using a Luttinger Ward scheme for interacting gauge particles, we present a conserving many body treatment of a family of fully screened infinite U Anderson models that has a smooth cross-over into the Fermi liquid state, with a finite scattering phase shift at zero temperature and a Wilson ratio greater than one. We illustrate our method, computing the temperature dependence of the thermodynamics, resistivity and electron dephasing rate and discuss its future application to non-equilibrium quantum dots and quantum critical mixed valent systems