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.
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.
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.
Predicting the physical properties of strongly correlated electron systems (SCES) requires the combined Density Functional Theory and Dynamical Mean-Field Theory (DFT+DMFT) framework. However, the computational bottle-neck lies in the impurity solver. This work focuses on rigorously benchmarking the Multi-Orbital Iterated Perturbation Theory (MO-IPT) impurity solver against the numerically exact Continuous-Time Quantum Monte Carlo (CTQMC) method, specifically through a detailed study of the three-orbital Hubbard model. The two-orbital model serves as a canonical system to test performance under realistic multi-band conditions. Our systematically derived MO-IPT overcomes the critical limitations of CTQMC, including exponential scaling with orbital number, the need for analytic continuation, and the severe fermionic sign problem. By demonstrating high accuracy across varying interaction strengths and temperatures, we validate MO-IPT as an inexpensive, yet reliable, replacement solver essential for future material-specific investigations.
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.
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.
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.
We present two related customized software packages, Hubb_DMFT and Wan2mb_DMFT, designed to solve the Dynamical Mean-Field Theory (DMFT) equations for strongly correlated electron systems. Hubb_DMFT is adjusted for the single-band Hubbard model, providing a fast way to calculate the local self-energy, as well as the two-particle fermion and triangular fermion-boson charge and spin vertices, while Wan2mb_DMFT extends this capability to realistic multi-orbital systems, directly interfacing Wannier tight-binding Hamiltonians with many-body solvers. Both codes are based on iQIST v.0.7 impurity solver and utilize a modified and internally integrated Continuous-Time Quantum Monte Carlo (CT-QMC) core with the hybridization expansion (CT-HYB) framework and improved self-energy and vertex estimators for density-density interaction, ensuring numerically exact solutions for quantum impurity problems.