arXiv subjects

Olivier Parcollet

Publications and source records attributed to Olivier Parcollet.

At least 55 records · Page 3Linked to original sources

arXiv2019

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.

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arXiv2019

Hall coefficient signals orbital differentiation in the Hund's metal Sr$_2$RuO$_4$

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.

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arXiv2019

Cancellation of vacuum diagrams and long-time limit in out-of-equilibrium diagrammatic Quantum Monte Carlo

We express the recently introduced real-time diagrammatic Quantum Monte Carlo, Phys. Rev. B 91, 245154 (2015), in the Larkin-Ovchinnikov basis in Keldysh space. Based on a perturbation expansion in the local interaction $U$, the special form of the interaction vertex allows to write diagrammatic rules in which vacuum Feynman diagrams directly vanish. This reproduces the main property of the previous algorithm, without the cost of the exponential sum over Keldysh indices. In an importance sampling procedure, this implies that only interaction times in the vicinity of the measurement time contribute. Such an algorithm can then directly address the long-time limit needed in the study of steady states in out-of-equilibrium systems. We then implement and discuss different variants of Monte Carlo algorithms in the Larkin-Ovchinnikov basis. A sign problem reappears, showing that the cancellation of vacuum diagrams has no direct impact on it.

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arXiv2019

Magnetic response of Sr$_2$RuO$_4$: quasi-local spin fluctuations due to Hund's coupling

We study the magnetic susceptibility in the normal state of Sr$_2$RuO$_4$ using dynamical mean-field theory including dynamical vertex corrections. Besides the well known incommensurate response, our calculations yield quasi-local spin fluctuations which are broad in momentum and centered around the $Γ$ point, in agreement with recent inelastic neutron scattering experiments [P. Steffens, et al., Phys. Rev. Lett. 122, 047004 (2019)]. We show that these quasi-local fluctuations are controlled by the Hund's coupling and account for the dominant contribution to the momentum-integrated response. While all orbitals contribute equally to the incommensurate response, the enhanced $Γ$ point response originates from the planar xy orbital.

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arXiv2018

Resonant thermalization of periodically driven strongly correlated electrons

We study the dynamics of the Fermi-Hubbard model driven by a time-periodic modulation of the interaction within nonequilibrium Dynamical Mean-Field Theory. For moderate interaction, we find clear evidence of thermalization to a genuine infinite-temperature state with no residual oscillations. Quite differently, in the strongly correlated regime, we find a quasi-stationary extremely long-lived state with oscillations synchronized with the drive (Floquet prethermalization). Remarkably, the nature of this state dramatically changes upon tuning the drive frequency. In particular, we show the existence of a critical frequency at which the system rapidly thermalizes despite the large interaction. We characterize this resonant thermalization and provide an analytical understanding in terms of a break down of the periodic Schrieffer-Wolff transformation.

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arXiv2018

Practical consequences of Luttinger-Ward functional multivaluedness for cluster DMFT methods

The Luttinger-Ward functional (LWF) has been a starting point for conserving approximations in many-body physics for 50 years. The recent discoveries of its multivaluedness and the associated divergence of the two-particle irreducible vertex function $Γ$ have revealed an inherent limitation of this approach. Here we demonstrate how these undesirable properties of the LWF can lead to a failure of computational methods based on an approximation of the LWF. We apply the Nested Cluster Scheme (NCS) to the Hubbard model and observe the existence of an additional stationary point of the self-consistent equations, associated with an unphysical branch of the LWF. In the strongly correlated regime, starting with the first divergence of $Γ$, this unphysical stationary point becomes attractive in the standard iterative technique used to solve DMFT. This leads to an incorrect solution, even in the large cluster size limit, for which we discuss diagnostics.

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arXiv2017

Spin-Orbit Coupling and Electronic Correlations in Sr2RuO4

We investigate the interplay of spin-orbit coupling (SOC) and electronic correlations in Sr2RuO4 using dynamical mean-field theory. We find that SOC does not affect the correlation-induced renormalizations, which validates the Hund's metal picture of ruthenates even in the presence of the sizable SOC relevant to these materials. Nonetheless, SOC found to change significantly the electronic structure at k-points where a degeneracy applies in its absence. We explain why these two observations are consistent with one another and calculate effects of SOC on the correlated electronic structure. The magnitude of these effects is found to depend on the energy of the quasiparticle state under consideration, leading us to introduce the notion of an "energy-dependent quasiparticle spin-orbit coupling". This notion is generally applicable to all materials in which both the spin-orbit coupling and electronic correlations are sizable.

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arXiv2017

Chiral d-wave Superconductivity in a Triangular Surface Lattice Mediated by Long-range Interaction

Correlated ad-atom systems on the Si(111) surface have recently attracted an increased attention as strongly correlated systems with a rich phase diagram. We study these materials by a single band model on the triangular lattice including 1/r long-range interaction. Employing the recently proposed TRILEX method we find an unconventional superconducting phase of chiral d-wave symmetry in hole-doped systems. The superconductivity is driven simultaneously by both charge and spin fluctuations and is strongly enhanced by the long-range tail of the interaction. We provide an analysis of the relevant collective bosonic modes and explain how in triangular symmetry both charge and spin channels contribute to the Cooper-pairing.

cond-mat.supr-con↗

arXiv2017

TRILEX and $GW$+EDMFT approach to $d$-wave superconductivity in the Hubbard model

We generalize the recently introduced TRILEX approach (TRiply Irreducible Local EXpansion) to superconducting phases. The method treats simultaneously Mott and spin-fluctuation physics using an Eliashberg theory supplemented by local vertex corrections determined by a self-consistent quantum impurity model. We show that, in the two-dimensional Hubbard model, at strong coupling, TRILEX yields a $d$-wave superconducting dome as a function of doping. Contrary to the standard cluster dynamical mean field theory (DMFT) approaches, TRILEX can capture $d$-wave pairing using only a single-site effective impurity model. We also systematically explore the dependence of the superconducting temperature on the bare dispersion at weak coupling, which shows a clear link between strong antiferromagnetic (AF) correlations and the onset of superconductivity. We identify a combination of hopping amplitudes particularly favorable to superconductivity at intermediate doping. Finally, we study within $GW$+EDMFT the low-temperature $d$-wave superconducting phase at strong coupling in a region of parameter space with reduced AF fluctuations.

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arXiv2017

Renormalization of effective interactions in a negative charge-transfer insulator

We compute from first principles the effective interaction parameters appropriate for a low-energy description of the rare-earth nickelate LuNiO$_{3}$ involving the partially occupied $e_g$ states only. The calculation uses the constrained random-phase approximation and reveals that the effective on-site Coulomb repulsion is strongly reduced by screening effects involving the oxygen-$p$ and nickel-$t_{2g}$ states. The long-range component of the effective low-energy interaction is also found to be sizeable. As a result, the effective on-site interaction between parallel-spin electrons is reduced down to a small negative value. This validates effective low-energy theories of these materials proposed earlier. Electronic structure methods combined with dynamical mean-field theory are used to construct and solve an appropriate low-energy model and explore its phase diagram as a function of the on-site repulsion and Hund's coupling. For the calculated values of these effective interactions we find, in agreement with experiments, that LuNiO$_{3}$ is a metal without disproportionation of the $e_g$ occupancy when considered in its orthorhombic structure, while the monoclinic phase is a disproportionated insulator.

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arXiv2017

The Fierz convergence criterion: a controlled approach to strongly-interacting systems with small embedded clusters

We present an embedded-cluster method, based on the TRILEX formalism. It turns the Fierz ambiguity, inherent to approaches based on a bosonic decoupling of local fermionic interactions, into a convergence criterion. It is based on the approximation of the three-leg vertex by a coarse-grained vertex computed by solving a self-consistently determined multi-site effective impurity model. The computed self-energies are, by construction, continuous functions of momentum. We show that, in three interaction and doping regimes of parameters of the two-dimensional Hubbard model, self-energies obtained with clusters of size four only are very close to numerically exact benchmark results. We show that the Fierz parameter, which parametrizes the freedom in the Hubbard-Stratonovich decoupling, can be used as a quality control parameter. By contrast, the $GW$+extended dynamical mean field theory approximation with four cluster sites is shown to yield good results only in the weak-coupling regime and for a particular decoupling. Finally, we show that the vertex has spatially nonlocal components only at low Matsubara frequencies.

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arXiv2016

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

We 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$Γ$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$Γ$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.

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arXiv2016

Enhancing superconductivity in A3C60 fullerides

Motivated by the recent experimental report of a possible light-induced superconductivity in A3C60 at high temperature [Mitrano et al., Nature 530, 451 (2016)], we investigate theoretical mechanisms for enhanced superconductivity in A3C60 fullerenes. We find that an `interaction imbalance' corresponding to a smaller value of the Coulomb matrix element for two of the molecular orbitals in comparison to the third one, efficiently enhances superconductivity. Furthermore, we perform first-principle calculations of the changes in the electronic structure and in the screened Coulomb matrix elements of A3C60, brought in by the deformation associated with the pumped T1u intra-molecular mode. We find that an interaction imbalance is indeed induced, with a favorable sign and magnitude for superconductivity enhancement. The physical mechanism responsible for this enhancement consists in a stabilisation of the intra-molecular states containing a singlet pair, while preserving the orbital fluctuations allowing for a coherent inter-orbital delocalization of the pair. Other perturbations have also been considered and found to be detrimental to superconductivity. The light-induced deformation and ensuing interaction imbalance is shown to bring superconductivity further into the strong-coupling regime.

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arXiv2016

Large effects of subtle electronic correlations on the energetics of vacancies in alpha-Fe

We study the effect of electronic Coulomb correlations on the vacancy formation energy in paramagnetic alpha-Fe within ab initio dynamical mean-field theory. The calculated value for the formation energy is substantially lower than in standard density-functional calculations and in excellent agreement with experiment. The reduction is caused by an enhancement of electronic correlations at the nearest neighbors of the vacancy. This effect is explained by subtle changes in the corresponding spectral function of the d-electrons. The local lattice relaxations around the vacancy are substantially increased by many-body effects.

cond-mat.str-el↗

arXiv2016

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 $Λ(iω,iΩ)$, 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.

cond-mat.str-el↗

arXiv2016

TRIQS/DFTTools: A TRIQS application for ab initio calculations of correlated materials

We present the TRIQS/DFTTools package, an application based on the TRIQS library that connects this toolbox to realistic materials calculations based on density functional theory (DFT). In particular, TRIQS/DFTTools together with TRIQS allows an efficient implementation of DFT plus dynamical mean-field theory (DMFT) calculations. It supplies tools and methods to construct Wannier functions and to perform the DMFT self-consistency cycle in this basis set. Post-processing tools, such as band-structure plotting or the calculation of transport properties are also implemented. The package comes with a fully charge self-consistent interface to the Wien2k band structure code, as well as a generic interface that allows to use TRIQS/DFTTools together with a large variety of DFT codes. It is distributed under the GNU General Public License (GPLv3).

cond-mat.str-el↗

arXiv2015

TRIQS: A Toolbox for Research on Interacting Quantum Systems

We present the TRIQS library, a Toolbox for Research on Interacting Quantum Systems. It is an open-source, computational physics library providing a framework for the quick development of applications in the field of many-body quantum physics, and in particular, strongly-correlated electronic systems. It supplies components to develop codes in a modern, concise and efficient way: e.g. Green's function containers, a generic Monte Carlo class, and simple interfaces to HDF5. TRIQS is a C++/Python library that can be used from either language. It is distributed under the GNU General Public License (GPLv3). State-of-the-art applications based on the library, such as modern quantum many-body solvers and interfaces between density-functional-theory codes and dynamical mean-field theory (DMFT) codes are distributed along with it.

cond-mat.str-el↗

arXiv2015

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.

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