Recent years have seen a rise in the popularity of the physics of strongly interacting electronic systems, and in most of the more interesting cases the perturbative regime is not applicable. The continuous-time quantum Monte Carlo (CT-QMC) has already established its leading stochastic simulation method to address quantum impurity models that have gained central focus of DMFT. Lugiato-Lefever function approach, on the one hand, can provide a rigorous account of the electronic structure, excitation spectrum and phenomenon of correlation to most of the many-body systems. In the paper the connection between the CT-QMC technique and theory of Green functions are stated with a specification in the connection of the two, complementing each other in the solving of quantum many-body problems. We present the approach of CT-QMC that is numerically inexpensive but computes Green functions directly in the imaginary time that you then analytically continue to the real frequencies to obtain physical observables. Further, we discuss the ability to investigate quasiparticle behaviour, spectral density and transport phenomenon through self-energies acquired as Green functions in CT-QMC.
Recent years have seen a rise in the popularity of the physics of strongly interacting electronic systems, and in most of the more interesting cases the perturbative regime is not applicable. The continuous-time quantum Monte Carlo (CT-QMC) has already established its leading stochastic simulation method to address quantum impurity models that have gained central focus of DMFT. Lugiato-Lefever function approach, on the one hand, can provide a rigorous account of the electronic structure, excitation spectrum and phenomenon of correlation to most of the many-body systems. In the paper the connection between the CT-QMC technique and theory of Green functions are stated with a specification in the connection of the two, complementing each other in the solving of quantum many-body problems. We present the approach of CT-QMC that is numerically inexpensive but computes Green functions directly in the imaginary time that you then analytically continue to the real frequencies to obtain physical observables. Further, we discuss the ability to investigate quasiparticle behaviour, spectral density and transport phenomenon through self-energies acquired as Green functions in CT-QMC.
Dynamical mean-field theory (DMFT) is one of the most widely-used methods to treat accurately electron correlation effects in ab-initio real material calculations. Many modern large-scale implementations of DMFT in electronic structure codes involve solving a quantum impurity model with a continuous-time quantum Monte Carlo (CT-QMC) solver [Rubtsov et al., Phys. Rev. B 72, 035122 (2005); Werner et al., Phys. Rev. Lett. 97, 076405 (2006); Werner and Millis, Phys. Rev. B 74, 155107 (2006); Gull et al., Rev. Mod. Phys. 83, 349 (2011)]. The main advantage of CT-QMC is that, unlike standard quantum Monte Carlo approaches, it is able to generate the local Green's functions $G(\ensuremath{\tau})$ of the correlated system on an arbitrarily fine imaginary time $\ensuremath{\tau}$ grid, and is free of any systematic errors. In this work, we extend a hybrid QMC solver proposed by Khatami et al. [Phys. Rev. E 81, 056703 (2010)] and Rost et al. [Phys. Rev. E 87, 053305 (2013)] to a multiorbital context. This has the advantage of enabling impurity solver QMC calculations to scale linearly with inverse temperature $\ensuremath{\beta}$, and permit its application to d- and f-band materials. In addition, we present a Green's-function processing scheme which generates accurate quasicontinuous imaginary time solutions of the impurity problem which overcome errors inherent to standard QMC approaches. This solver and processing scheme are incorporated into a full DFT+DMFT calculation using the castep DFT code [Clark et al., Z. Kristallogr. 220, 567 (2005)]. Benchmark calculations for SrVO3 properties are presented. The computational efficiency of this method is also demonstrated.
We assess the continuous-time quantum Monte Carlo (CT-QMC) technique with hybridization expansion for solvingthe electronic structure of the strongly correlated system LaxSr1−xVO3 . The impurity solver method implemented here shows the fair agreement with the other available Monte Carlo techniques. From the study, it is found that the CT-QMC technique clearly distinguishes metallic phase, quasiparticle phase and insulating phases of the system depending upon the strength of the correlation. In case of La0.33Sr0.67VO3 system the metal-insulator transition is found to be at U = 4.5 eV for β = 6(eV)−1. The value of U depends with the value of β, and also the value of Hund’s coupling (J) and bandwidth (W). This technique allows the particle to exchange with the reservoir of the particles and the impurity sites, which is accounted numerically to treat the temporal fluctuation of the fermionic systems termed as dynamical mean field theory (DMFT). This theory is used to explain the phenomena of MottHubbard metal insulator transition of the materials which are applicable for designing the Mottronics, Neuromorphic computing, Quantum computing and resistive memory devices.
The acceleration of exact continuous time quantum Monte Carlo (CTQMC) approaches in multi-site or multi-orbital systems is extremely interesting work, because these approaches are very time-consuming in terms of numerical computation and might account for the nature of exotic behaviors such as high-temperature superconductivity and Mott insulator behavior observed in the strongly correlated materials. We extend the recently developed interaction-expansion CTQMC method in combination with a machine learning (CTQMC+ML) approach for the single-site and single-orbital systems to multi-site and multi-orbital ones. This method can be applied to explore the nonlocal correlation effects in lattice models and to study the electronic structure of real materials via an ab-initio density functional theory plus dynamical mean field theory approach. We find that our CTQMC+ML method for multi-site (and multi-orbital) systems accurately predicts the impurity Green’s function with less computational time than the CTQMC approaches, as in the case of the single-site and single-orbital version.
A novel scheme to solve the quantum eigenvalue problem through the imaginary-time Green function Monte Carlo method is presented. This method is applicable not only to the ground states, but also to the excited states of generic system. We demonstrate the actual utility of the method with the numerical examples on three simple systems. Typeset using REVTEX 1 The stochastic quantization has been successfully applied in recent years to the various problems of physics ranging from quantum chromo dynamics to the plasmon oscillation [1-3]. While it can handle very complex systems which is usually beyond the approach either by the direct diagonalization or by the perturbation, it has been only applicable to the calculation of the ground state properties of the system. In this paper, we propose a new method based on the imaginary-time Green function Monte Carlo approach, which is extendable to the excited states of Hamiltonian system. We have primarily in mind the non-relativistic quantum few body problem such as encountered in nuclear physics [4-6].
Abstract: Originally designed for the study of strong electronic correlations in model Hamiltonians, dynamical mean field theory (DMFT) has become, in combination with density functional theory (DFT), a powerful tool for ab initio simulations of real materials. At the heart of DMFT lies the solution of a quantum impurity problem. While only the continuous-time quantum Monte Carlo (CT-QMC) impurity solvers yield (statistically) exact solutions of a general impurity problem, they are quite complex and computationally expensive. Hence, in this thesis we are interested in improving the CT-QMC impurity solvers. After a short introduction to DMFT and its cluster extensions, we begin by reviewing two of the CT-QMC impurity solvers, the interaction expansion or “Rubtsov” solver (CT- INT) and the hybridization expansion solver (CT-HYB). Focussing on the latter, which is the algorithm of choice within real material simulations, we then show how to reduce a sign problem, allowing us to address the unusual criticality found in layered organic superconductors. With high-T c superconductivity as example, we further discuss how to ensure ergodicity of the CT-HYB solver in the context of broken symmetries. Finally, algorithmic optimizations of CT-HYB are presented and combined, leading to speedups of up to 500 within the context of real material simulations. // Résumé: Initialement conçue pour traiter les fortes corrélations électroniques dans des hamiltoniens modèles, la théorie du champ moyen dynamique (DMFT) est devenue, en combinaison avec la théorie de la densité fonctionnelle (DFT), un outil puissant pour la simulation de matériaux réels. Au cœur de la DMFT se trouve la solution d'un modèle d'impureté quantique. Seulement les solutionneurs d'impureté Monte Carlo en temps continu (CT-QMC) donnent des solutions exactes. En même temps, ces solutionneurs sont plutôt complexes et gourmands en temps de calcul. Le but de cette thèse est donc d'améliorer les solutionneurs d'impureté CT-QMC. Après une courte introduction à la DMFT et à ses extensions pour les amas, on commence par une revue de deux des solutionneurs CT-QMC, celui en développement d'interaction ou de "Rubtsov" (CT-INT) et celui en développement d'hybridation (CT-HYB). Mettant l'accent sur le dernier, qui est l'algorithme de choix dans le cadre des matériaux réels, on montre alors comment réduire un problème de signe, nous permettant ainsi de traiter la criticalité inhabituelle des organiques en couche. Avec la supraconductivité à haute température critique comme exemple, on discute ensuite comment assurer l'ergodicité du solutionneur CT-HYB dans le cadre des symétries brisées. Finalement, des optimisations algorithmiques sont présentées et combinées, amenant à des accélérations allant jusqu'à un facteur de 500 dans le contexte des matériaux réels.
An acceleration of continuous time quantum Monte Carlo (CTQMC) methods is a potentially interesting branch of work as they are matchless as impurity solvers of a dynamical mean field theory (DMFT) approach for the description of strongly correlated systems. The inversion of the $k\ifmmode\times\else\texttimes\fi{}k$ matrix with k2 operations given by the diagram expansion order k in the CTQMC fast update and the multiplication of the $k\ifmmode\times\else\texttimes\fi{}k$ matrix, and the noninteracting properties with $k\ifmmode\times\else\texttimes\fi{}{\ensuremath{\omega}}_{{n}_{\text{max}}}^{m\ensuremath{-}1}$ operations to measure the m-point correlators, are computationally time consuming. Here we propose the CTQMC method in combination with a machine learning technique, which eliminates the $k\ifmmode\times\else\texttimes\fi{}{\ensuremath{\omega}}_{{n}_{\text{max}}}$ and $k\ifmmode\times\else\texttimes\fi{}{\ensuremath{\omega}}_{{n}_{\text{max}}}^{3}$ operations for the two-point impurity Green's functions ${G}_{\ensuremath{\sigma}}(i{\ensuremath{\omega}}_{n})$ and four-point vertices ${\ensuremath{\chi}}_{\ensuremath{\sigma},\overline{\ensuremath{\sigma}}}(i{\ensuremath{\omega}}_{n{}_{1}},i{\ensuremath{\omega}}_{n{}_{2}},i{\ensuremath{\omega}}_{n{}_{3}},i{\ensuremath{\omega}}_{n{}_{4}})$, respectively. This method not only predicts the accurate physical properties at low temperature, but also dramatically decreases the computational times of ${\ensuremath{\chi}}_{\ensuremath{\sigma},\overline{\ensuremath{\sigma}}}(i{\ensuremath{\omega}}_{n{}_{1}},i{\ensuremath{\omega}}_{n{}_{2}},i{\ensuremath{\omega}}_{n{}_{3}},i{\ensuremath{\omega}}_{n{}_{4}})$ for the nonlocal extension of DMFT approximation.