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We present a numerically exact steady-state inchworm Monte Carlo method for nonequilibrium quantum impurity models. Rather than propagating an initial state to long times, the method is directly formulated in the steady-state. This eliminates any need to traverse the transient dynamics and grants access to a much larger range of parameter regimes at vastly reduced computational costs. We benchmark the method on equilibrium Green's functions of quantum dots in the noninteracting limit and in the unitary limit of the Kondo regime. We then consider correlated materials described with dynamical mean field theory and driven away from equilibrium by a bias voltage. We show that the response of a correlated material to a bias voltage differs qualitatively from the splitting of the Kondo resonance observed in bias-driven quantum dots.

Finite-temperature quantum field theories are formulated in terms of Green's functions and self-energies on the Matsubara axis. In multi-orbital systems, these quantities are related to positive semidefinite matrix-valued functions of the Carath��odory and Schur class. Analysis, interpretation and evaluation of derived quantities such as real-frequency response functions requires analytic continuation of the off-diagonal elements to the real axis. We derive the criteria under which such functions exist for given Matsubara data and present an interpolation algorithm that intrinsically respects their mathematical properties. For small systems with precise Matsubara data, we find that the continuation exactly recovers all off-diagonal and diagonal elements. In real-materials systems, we show that the precision of the continuation is sufficient for the analytic continuation to commute with the Dyson equation, and we show that the commonly used truncation of off-diagonal self-energy elements leads to considerable approximation artifacts. Our method paves the way for the systematic evaluation of Matsubara data with equations of many-body theory on the real-frequency axis.

Since in periodic systems, a given element may be present in different spatial arrangements displaying vastly different physical and chemical properties, an elemental basis set that is independent of physical properties of materials may lead to significant simulation inaccuracies. To avoid such a lack of material specificity within a given basis set, we present a material-specific Gaussian basis optimization scheme for solids, which simultaneously minimizes the total energy of the system and optimizes the band energies when compared to the reference plane wave calculation while taking care of the overlap matrix condition number. To assess this basis set optimization scheme, we compare the quality of the Gaussian basis sets generated for diamond, graphite, and silicon via our method against the existing basis sets. The optimization scheme of this work has also been tested on the existing Gaussian basis sets for periodic systems such as MoS$_2$ and NiO yielding improved results.

The accurate determination of magnetic phase transitions in electronic systems is an important task of solid state theory. While numerically exact results are readily available for model systems such as the half-filled 3D Hubbard model, the complexity of real materials requires additional approximations, such as the restriction to certain classes of diagrams in perturbation theory, that reduce the precision with which magnetic properties are described. In this work, we examine the description of magnetic properties in second order perturbation theory, GW, FLEX, and two TMatrix approximations to numerically exact CT-QMC reference data. We assess finite-size effects and compare periodic lattice simulations to cluster embedding. We find that embedding substantially improves finite size convergence. However, by analyzing different partial summation methods we find no systematic improvement in the description of magnetic properties, with most methods considered in this work predicting first-order instead of continuous transitions, leading us to the conclusion that non-perturbative methods are necessary for the accurate determination of magnetic properties and phase transitions., Comment: 14 pages, 12 figures

We present an implementation of a fully self-consistent finite temperature second order Green's function perturbation theory (GF2) within the diagrammatic Monte Carlo framework. In contrast to the previous implementations of stochastic GF2 ({\it J. Chem. Phys.},{\bf 151}, 044144 (2019)), the current self-consistent stochastic GF2 does not introduce a systematic bias of the resulting electronic energies. Instead, the introduced implementation accounts for the stochastic errors appearing during the solution of the Dyson equation. We present an extensive discussion of the error handling necessary in a self-consistent procedure resulting in dressed Green's function lines. We test our method on a series of simple molecular examples.

A theoretical understanding of the enigmatic linear-in-temperature ($T$) resistivity, ubiquitous in strongly correlated metallic systems, has been a long sought-after goal. Furthermore, the slope of this robust $T$-linear resistivity is also observed to stay constant through crossovers between different temperature regimes: a phenomenon we dub "slope invariance". Recently, several solvable models with $T$-linear resistivity have been proposed, putting us in an opportune moment to compare their inner workings in various explicit calculations. We consider two strongly correlated models with local self-energies that demonstrate $T$-linearity: a lattice of coupled Sachdev-Ye-Kitaev (SYK) models and the Hubbard model in single-site dynamical mean-field theory (DMFT). We find that the two models achieve $T$-linearity through distinct mechanisms at intermediate temperatures. However, we also find that these mechanisms converge to an identical form at high temperatures. Surprisingly, both models exhibit "slope invariance" across the two temperature regimes. We thus not only reveal some of the diversity in the theoretical inner workings that can lead to $T$-linear resistivity, but we also establish that different mechanisms can result in "slope invarance".

The nonequilibrium spectral properties of the Anderson impurity model with a chemical potential bias are investigated within a numerically exact real time quantum Monte Carlo formalism. The two-time correlation function is computed in a form suitable for nonequilibrium dynamical mean field calculations. Additionally, the evolution of the model's spectral properties are simulated in an alternative representation, defined by a hypothetical but experimentally realizable weakly coupled auxiliary lead. The voltage splitting of the Kondo peak is confirmed and the dynamics of its formation after a coupling or gate quench are studied. This representation is shown to contain additional information about the dot's population dynamics. Further, we show that the voltage-dependent differential conductance gives a reasonable qualitative estimate of the equilibrium spectral function, but significant qualitative differences are found including incorrect trends and spurious temperature dependent effects.

Cluster dynamical mean field and maximum entropy analytical continuation methods are used to obtain theoretical estimates for the many-body density of states, electron self-energy, in-plane and c-axis optical conductivity and the $B_{1g}$ and $B_{2g}$ Raman scattering spectra of the two dimensional square lattice Hubbard model at intermediate interaction strengths and carrier concentrations near half filling. The calculations are based on an 8-site cluster approximation which gives access to both the zone-diagonal and zone-face portions of the Fermi surface. At low dopings the zone-face regions exhibit a 'pseudogap', a suppression of the many-body density of states for energies near the Fermi surface. The pseudogap magnitude is largest near half filling and decreases smoothly with doping, but as temperature is increased the gap fills in rather than closes. The calculated response functions bear a strong qualitative resemblance to data taken in the pseudogap regime of high-$T_c$ cuprates, strongly suggesting that the intermediate coupling Hubbard model accounts for much of the exotic behavior observed in high-$T_c$ materials., Comment: 12 pages, 15 figures, minor changes from previous version in response to referee reports

Metal-insulator transitions in the paramagnetic phase of the two dimensional square lattice Hubbard model are studied using the dynamical cluster approximation with eight momentum cells. We show that both the interaction-driven and the doping-driven transition are multi-stage and momentum-sector specific, with Fermi liquid metal and fully gapped insulator phases separated by an intermediate phase in which some regions of the Brillouin zone are gapped while others sustain gapless quasiparticles. We argue that this is the coarse-grained version of a gradually shrinking arc or pocket. A pronounced particle-hole asymmetry is found.

A single-site dynamical mean field study of a three band model with the rotationally invariant interactions appropriate to the t_2g levels of a transition metal oxide reveals a quantum phase transition between a paramagnetic metallic phase and an incoherent metallic phase with frozen moments. The Mott transitions occurring at electron densities n=2,3 per site take place inside the frozen moment phase. The critical line separating the two phases is characterized by a self energy with the frequency dependence \Sigma(\omega)\sim \sqrt{\omega} and a broad quantum critical regime. The findings are discussed in the context of the power law observed in the optical conductivity of SrRuO_3.

We study the anisotropic 3D Hubbard model with increased nearest neighbor tunneling amplitudes along one direction using the dynamical cluster approximation and compare the results to a quantum simulation experiment of ultracold fermions in an optical lattice. We find that the short range spin correlations are significantly enhanced in the direction with stronger tunneling amplitudes. Our results agree with the experimental observations and show that the experimental temperature is lower than the strong tunneling amplitude. We characterize the system by examining the spin correlations beyond neighboring sites and determine the distribution of density entropy and spin correlation in the trapped system. We furthermore investigate the dependence of the critical entropy at the Néel transition on anisotropy.