Worm-improved estimators in continuous-time quantum Monte Carlo

Gunacker, Patrik; Wallerberger, Markus; Ribic, T.; Hausoel, Andreas; Sangiovanni, Giorgio; Held, Karsten

doi:10.1103/physrevb.94.125153

Cited by 49 publications

(59 citation statements)

References 41 publications

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“…Particular attention has been devoted to the choice of the basis sets and the influence of the double counting. These steps have been made possible thanks to the parallel development of our code package "w2dynamics", developed in Würzburg, Bremen as well as in Vienna [27,114,115]. "w2dynamics", which will be made public in the course of 2017 [116], is a CT-QMC hybridization-expansion code, as described briefly in Section 3 and it allows users to set up calculations for big and complex realistic nanostructures in a rather flexible way.…”

Section: Discussionmentioning

confidence: 99%

Realistic theory of electronic correlations in nanoscopic systems

Schüler

Barthel

Wehling

et al. 2017

Eur. Phys. J. Spec. Top.

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Abstract.Nanostructures with open shell transition metal or molecular constituents host often strong electronic correlations and are highly sensitive to atomistic material details. This tutorial review discusses method developments and applications of theoretical approaches for the realistic description of the electronic and magnetic properties of nanostructures with correlated electrons. First, the implementation of a flexible interface between density functional theory and a variant of dynamical mean field theory (DMFT) highly suitable for the simulation of complex correlated structures is explained and illustrated. On the DMFT side, this interface is largely based on recent developments of quantum Monte Carlo and exact diagonalization techniques allowing for efficient descriptions of general four fermion Coulomb interactions, reduced symmetries and spin-orbit coupling, which are explained here. With the examples of the Cr (001) surfaces, magnetic adatoms, and molecular systems it is shown how the interplay of Hubbard U and Hund's J determines charge and spin fluctuations and how these interactions drive different sorts of correlation effects in nanosystems. Non-local interactions and correlations present a particular challenge for the theory of low dimensional systems. We present our method developments addressing these two challenges, i.e., advancements of the dynamical vertex approximation and a combination of the constrained random phase approximation with continuum medium theories. We demonstrate how non-local interaction and correlation phenomena are controlled not only by dimensionality but also by coupling to the environment which is typically important for determining the physics of nanosystems.a

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Section: Discussionmentioning

confidence: 99%

Realistic theory of electronic correlations in nanoscopic systems

Schüler

Barthel

Wehling

et al. 2017

Eur. Phys. J. Spec. Top.

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“…Furthermore, CT-QMC algorithms naturally operate in the imaginary time basis, requiring an extra Fourier transform to Matsubara frequencies. Intrinsic statistical uncertainties in the high-frequency region of the two-particle quantities 100,101) combined with the previously mentioned computational requirements limit us hence to small frequency box sizes of the two-particle Green's func- Fig. 2.…”

Section: Ct-qmc Calculation Of the Local Vertexmentioning

confidence: 99%

Towards ab initio Calculations with the Dynamical Vertex Approximation

et al. 2018

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While key effects of the many-body problem-such as Kondo and Mott physics-can be understood in terms of onsite correlations, non-local fluctuations of charge, spin, and pairing amplitudes are at the heart of the most fascinating and unresolved phenomena in condensed matter physics. Here, we review recent progress in diagrammatic extensions to dynamical mean-field theory for ab initio materials calculations. We first recapitulate the quantum field theoretical background behind the two-particle vertex. Next we discuss latest algorithmic advances in quantum Monte Carlo simulations for calculating such two-particle quantities using worm sampling and vertex asymptotics, before giving an introduction to the ab initio dynamical vertex approximation (AbinitioDΓA). Finally, we highlight the potential of AbinitioDΓA by detailing results for the prototypical correlated metal SrVO 3 .

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“…The exact procedure on how to define equal-time Green's function estimators can be found in previous works. 40 By adding the local creation and annihilation operators of the estimators to the local trace of the infinite perturbation series in the hybridization expansion, one effectively switches to worm space. We redefine the single-frequency expectation values in Eqs.…”

Section: Implementation a Worm Samplingmentioning

confidence: 99%

Continuous-time quantum Monte Carlo calculation of multiorbital vertex asymptotics

2017

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We derive the equations for calculating the high-frequency asymptotics of the local two-particle vertex function for a multi-orbital impurity model. These relate the asymptotics for a general local interaction to equal-time two-particle Green's functions, which we sample using continuoustime quantum Monte Carlo simulations with a worm algorithm. As specific examples we study the single-orbital Hubbard model and the three t2g orbitals of SrVO3 within dynamical mean field theory (DMFT). We demonstrate how the knowledge of the high-frequency asymptotics reduces the statistical uncertainties of the vertex and further eliminates finite box size effects. The proposed method benefits the calculation of non-local susceptibilities in DMFT and diagrammatic extensions of DMFT.

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Worm-improved estimators in continuous-time quantum Monte Carlo

Cited by 49 publications

References 41 publications

Realistic theory of electronic correlations in nanoscopic systems

Realistic theory of electronic correlations in nanoscopic systems

Towards ab initio Calculations with the Dynamical Vertex Approximation

Continuous-time quantum Monte Carlo calculation of multiorbital vertex asymptotics

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