arXiv subjects

Philipp Werner

Publications and source records attributed to Philipp Werner.

At least 217 records · Page 12Linked to original sources

arXiv2015

Nonequilibrium dynamical cluster theory

We study the effect of spatially nonlocal correlations on the nonequilibrium dynamics of interacting fermions by constructing the nonequilibrium dynamical cluster theory, a cluster generalization of the nonequilibrium dynamical mean-field theory (DMFT). The formalism is applied to interaction quenches in the Hubbard model in one and two dimensions, and the results are compared with data from single-site DMFT, the time-dependent density matrix renormalization group, and lattice perturbation theory. Both in one and two dimensions the double occupancy quickly thermalizes, while the momentum distribution relaxes only on much longer time scales. For the two-dimensional square lattice we find a strongly momentum-dependent evolution of the momentum distribution around the Fermi energy, with a much faster relaxation near the momenta $(0,π)$ and $(π,0)$ than near $(π/2,π/2)$. This result is interpreted as reflecting the momentum-anisotropic quasiparticle lifetime of the marginal Fermi liquid. The method is further applied to the two-dimensional Hubbard model driven by a dc electric field, where the damping of the Bloch oscillation of the current is found to be less effective than predicted by DMFT and lattice perturbation theory.

cond-mat.str-el↗

arXiv2015

On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime

We study the two-dimensional Hubbard model in the weak-coupling regime and compare the self-energy obtained from various approximate diagrammatic schemes to the result of diagrammatic Monte Carlo simulations, which sum up all weak-coupling diagrams up to a given order. While dynamical mean-field theory provides a good approximation for the local part of the self-energy, including its frequency dependence, the partial summation of bubble and/or ladder diagrams typically yields worse results than second order perturbation theory. Even widely used self-consistent schemes such as GW or the fluctuation-exchange approximation (FLEX) are found to be unreliable. Combining the dynamical mean-field self-energy with the nonlocal component of GW in GW+DMFT yields improved results for the local self-energy and nonlocal self-energies of the correct order of magnitude, but here, too, a more reliable scheme is obtained by restricting the nonlocal contribution to the second order diagram. FLEX+DMFT is found to give accurate results in the low-density regime, but even worse results than FLEX near half-filling.

cond-mat.str-el↗

arXiv2015

Orbital-Selective Mott Transition and Evolution of the Zhang-Rice State in Cubic Phase UO$_{2}$ Under Pressure

We study the electronic structure of cubic phase uranium dioxide at different volumes using a combination of density functional theory and dynamical mean-field theory. The \emph{ab initio} calculations predict an orbital-selective Mott insulator-metal transition at a moderate pressure of $\approx 45$ GPa. At this pressure the $j=5/2$ states become metallic, while the $j=7/2$ states remain insulating up to about 60 GPa. In the metallic state, we observe a rapid decrease of the 5$f$ occupation and total angular momentum with pressure. Simultaneously, the generalized Zhang-Rice state, which is of predominantly $j=5/2$ character, quickly disappears after the transition into the metallic phase.

cond-mat.str-el↗

arXiv2015

Double-expansion impurity solver for multiorbital models with dynamically screened U and J

We present a continuous-time Monte Carlo impurity solver for multiorbital impurity models which combines a strong-coupling hybridization expansion and a weak-coupling expansion in the Hund's coupling parameter J. This double-expansion approach allows to treat the dominant density-density interactions U within the efficient segment representation. We test the approach for a two-orbital model with static interactions, and then explain how the double-expansion allows to simulate models with frequency dependent U(ω) and J(ω). The method is used to investigate spin state transitions in a toy model for fullerides, with repulsive bare J but attractive screened J.

cond-mat.str-el↗

arXiv2015

Accuracy of downfolding based on the constrained random phase approximation

We study the reliability of the constrained random phase approximation (cRPA) method for the calculation of low-energy effective Hamiltonians by considering multi-orbital lattice models with one strongly correlated "target" band and two weakly correlated "screening" bands. The full multi-orbital system and the effective model are solved within dynamical mean field theory (DMFT) in a consistent way. By comparing the quasi-particle weights for the correlated bands, we examine how accurately the effective model describes the low-energy properties of the multi-band system. We show that the violation of the Pauli principle in the cRPA method leads to overscreening effects when the inter-orbital interaction is small. This problem can be overcome by using a variant of the cRPA method which restores the Pauli principle.

cond-mat.str-el↗

arXiv2015

Non-thermal melting of Neel order in the Hubbard model

We study the unitary time evolution of antiferromagnetic order in the Hubbard model after a quench starting from the perfect Néel state. In this setup, which is well suited for experiments with cold atoms, one can distinguish fundamentally different pathways for melting of long-range order at weak and strong interaction. In the Mott insulating regime, melting of long-range order occurs due to the ultra-fast transfer of energy from charge excitations to the spin background, while local magnetic moments and their exchange coupling persist during the process. The latter can be demonstrated by a local spin-precession experiment. At weak interaction, local moments decay along with the long-range order. The dynamics is governed by residual quasiparticles, which are reflected in oscillations of the off-diagonal components of the momentum distribution. Such oscillations provide an alternative route to study the prethermalization phenomenon and its influence on the dynamics away from the integrable (noninteracting) limit. The Hubbard model is solved within nonequilibrium dynamical mean-field theory, using the density matrix-renormalization group as an impurity solver.

cond-mat.str-el↗

arXiv2015

Nonequilibrium dynamical mean-field theory for bosonic lattice models

We develop the nonequilibrium extension of bosonic dynamical mean field theory (BDMFT) and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong coupling perturbative approaches, nonequilibrium BDMFT captures not only dynamical transitions, but also damping and thermalization effects at finite temperature. We apply the formalism to quenches in the Bose-Hubbard model, starting both from the normal and Bose-condensed phases. Depending on the parameter regime, one observes qualitatively different dynamical properties, such as rapid thermalization, trapping in metastable superfluid or normal states, as well as long-lived or strongly damped amplitude oscillations. We summarize our results in non-equilibrium "phase diagrams" which map out the different dynamical regimes.

cond-mat.quant-gas↗

arXiv2015

$i$QIST: An open source continuous-time quantum Monte Carlo impurity solver toolkit

Quantum impurity solvers have a broad range of applications in theoretical studies of strongly correlated electron systems. Especially, they play a key role in dynamical mean-field theory calculations of correlated lattice models and realistic materials. Therefore, the development and implementation of efficient quantum impurity solvers is an important task. In this paper, we present an open source interacting quantum impurity solver toolkit (dubbed $i$QIST). This package contains several highly optimized quantum impurity solvers which are based on the hybridization expansion continuous-time quantum Monte Carlo algorithm, as well as some essential pre- and post-processing tools. We first introduce the basic principle of continuous-time quantum Monte Carlo algorithm and then discuss the implementation details and optimization strategies. The software framework, major features, and installation procedure for $i$QIST are also explained. Finally, several simple tutorials are presented in order to demonstrate the usage and power of $i$QIST.

cond-mat.str-el↗

arXiv2015

Superconductivity in the two-band Hubbard model

We study the two-band Hubbard model in infinite dimensions by solving the dynamical mean-field equations with a strong coupling continuous-time quantum Monte Carlo method and show that an $s$-wave superconducting state can be stabilized in the repulsively interacting case. We discuss how this superconducting state competes with the metallic and paired Mott states. The effects of the Hund coupling and crystalline electric field are also addressed.

cond-mat.str-el↗

arXiv2015

First order dynamical phase transitions

Recently, dynamical phase transitions have been identified based on the non-analytic behavior of the Loschmidt echo in the thermodynamic limit [Heyl et al., Phys.~Rev.~Lett.~{\bf 110}, 135704 (2013)]. By introducing conditional probability amplitudes, we show how dynamical phase transitions can be further classified, both mathematically, and potentially in experiment. This leads to the definition of first-order dynamical phase transitions. Furthermore, we develop a generalized Keldysh formalism which allows to use nonequilibrium dynamical mean-field theory to study the Loschmidt echo and dynamical phase transitions in high-dimensional, non-integrable models. We find dynamical phase transitions of first order in the Falicov-Kimball model and in the Hubbard model.

cond-mat.str-el↗

arXiv2014

Supersolid Phase Accompanied by a Quantum Critical Point in the Intermediate Coupling Regime of the Holstein Model

We reveal that electron-phonon systems described by the Holstein model on a bipartite lattice exhibit, away from half filling, a supersolid (SS) phase characterized by coexisting charge order (CO) and superconductivity (SC), and an accompanying quantum critical point (QCP). The SS, demonstrated by the dynamical mean-field theory with a quantum Monte Carlo impurity solver, emerges in the intermediate-coupling regime, where the peak of the Tc dome is located and the metal-insulator crossover occurs. On the other hand, in the weak- and strong-coupling regimes the CO-SC boundary is of first order with no intervening SS phases. The QCP is associated with the continuous transition from SS to SC and characterized by a reentrant behavior of the SS around it. We further show that the SS-SC transition is hallmarked by diverging charge fluctuations and a kink (peak) in the superfluid density.

cond-mat.str-el↗

arXiv2014

Role of impact ionization in the thermalization of photo-excited Mott insulators

We study the influence of the pulse energy and fluence on the thermalization of photo-doped Mott insulators. If the Mott gap is smaller than the width of the Hubbard bands, the kinetic energy of individual carriers can be large enough to produce doublon-hole pairs via a process analogous to impact ionization. The thermalization dynamics, which involves an adjustment of the doublon and hole densities, thus changes as a function of the energy of the photo-doped carriers and exhibits two timescales -- a fast relaxation related to impact ionization and a slower timescale associated with higher-order scattering processes. The slow dynamics depends more strongly on the gap size and the photo-doping concentration.

cond-mat.str-el↗

arXiv2014

Dynamical screening in La2CuO4

We show that the dynamical screening of the Coulomb interaction among Cu-d electrons in high-Tc cuprates is very strong and that a proper treatment of this effect is essential for a consistent description of the electronic structure. In particular, we find that ab-initio calculations for undoped La2CuO4 yield an insulator only if the frequency dependence of the Coulomb interaction is taken into account. We also identify a collective excitation in the screened interaction at 9 eV which is rather localized on the copper site, and which is responsible for a satellite structure at energy -13 eV, located below the p bands.

cond-mat.str-el↗

arXiv2014

Interaction quench in the Holstein model: Thermalization crossover from electron- to phonon-dominated relaxation

We study the relaxation of the Holstein model after a sudden switch-on of the interaction by means of the nonequilibrium dynamical mean field theory, with the self-consistent Migdal approximation as an impurity solver. We show that there exists a qualitative change in the thermalization dynamics as the interaction is varied in the weak-coupling regime. On the weaker interaction side of this crossover, the phonon oscillations are damped more rapidly than the electron thermalization timescale, as determined from the relaxation of the electron momentum distribution function. On the stronger interaction side, the relaxation of the electrons becomes faster than the phonon damping. In this regime, despite long-lived phonon oscillations, a thermalized momentum distribution is realized temporarily. The origin of the thermalization crossover found here is traced back to different behaviors of the electron and phonon self-energies as a function of the electron-phonon coupling. In addition, the importance of the phonon dynamics is demonstrated by comparing the self-consistent Migdal results with those obtained with a simpler Hatree-Fock impurity solver that neglects the phonon self-energy. The latter scheme does not properly describe the evolution and thermalization of isolated electron-phonon systems.

cond-mat.str-el↗

arXiv2014

Extended dynamical mean-field study of the Hubbard model with long range interactions

Using extended dynamical mean-field theory and its combination with the $GW$ approximation, we compute the phase diagrams and local spectral functions of the single-band extended Hubbard model on the square and simple cubic lattices, considering long range interactions up to the third nearest neighbors. The longer range interactions shift the boundaries between the metallic, charge-ordered insulating and Mott insulating phases, and lead to characteristic changes in the screening modes and local spectral functions. Momentum-dependent self-energy contributions enhance the correlation effects and thus compete with the additional screening effect from longer range Coulomb interactions. Our results suggest that the influence of longer range intersite interactions is significant, and that these effects deserve attention in realistic studies of correlated materials.

cond-mat.str-el↗

arXiv2014

Ultra-fast photo-carrier relaxation in Mott insulators with short-range spin correlations

We compute the time-resolved photoemission spectrum after photo-doping in a two-dimensional Mott-Hubbard insulator. We find that the relaxation rate of high-energy photo-doped electrons in the paramagnetic phase scales with the strength of the nearest-neighbor spin correlations, which implies a pronounced increase of the relaxation times with temperature and excitation density. Finite doping, in contrast, opens additional scattering channels and leads to a faster relaxation. To obtain our results we have implemented a nonequilibrium version of the dynamical cluster approximation (DCA), which, in contrast to single-site dynamical mean-field theory, captures the effect of short-range correlations.

cond-mat.str-el↗

arXiv2014

Extended Mean Field study of complex $ϕ^4$-theory at finite density and temperature

We review the Extended Mean Field Theory (EMFT) approximation and apply it to complex, scalar $ϕ^4$-theory on the lattice. We study the critical properties of the Bose condensation driven by a nonzero chemical potential $μ$ at both zero and nonzero temperature and determine the $(T,μ)$ phase diagram. The results are in very good agreement with recent Monte Carlo data for all parameter values considered. EMFT can be formulated directly in the thermodynamic limit which allows us to study lattice spacings for which Monte Carlo studies are not feasible with present techniques. We find that the EMFT approximation accurately reproduces many known phenomena of the exact solution, like the "Silver Blaze" behavior at zero temperature and dimensional reduction at finite temperature.

hep-lat↗

arXiv2014

Nonequilibrium dynamical mean-field theory and its applications

The study of nonequilibrium phenomena in correlated lattice systems has developed into an active and exciting branch of condensed matter physics. This research field provides rich new insights that could not be obtained from the study of equilibrium situations, and the theoretical understanding of the physics often requires the development of new concepts and methods. On the experimental side, ultra-fast pump-probe spectroscopies enable studies of excitation and relaxation phenomena in correlated electron systems, while ultra-cold atoms in optical lattices provide a new way to control and measure the time-evolution of interacting lattice systems with a vastly different characteristic timescale compared to electron systems. A theoretical description of these phenomena is challenging because, firstly, we have to compute the quantum-mechanical time-evolution of many-body systems out of equilibrium, and secondly, deal with strong-correlation effects which can be of nonperturbative nature. In this review, we discuss the nonequilibrium extension of the dynamical mean field theory (DMFT), which treats quantum fluctuations in the time domain and works directly in the thermodynamic limit. The method reduces the complexity of the calculation via a mapping to a self-consistent impurity problem. Particular emphasis is placed on a detailed derivation of the formalism, and on a discussion of numerical techniques, which enable solutions of the effective nonequilibrium DMFT impurity problem. We summarize the insights gained into the properties of the infinite-dimensional Hubbard model under strong non-equilibrium conditions. These examples illustrate the current ability of the theoretical framework to reproduce and understand fundamental nonequilibrium phenomena, such as the dielectric breakdown of Mott insulators, photo-doping, and collapse-and-revival oscillations in quenched systems.

cond-mat.str-el↗