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arXiv:1109.4056 · Physical Review B

Efficient treatment of the high-frequency tail of the self-energy function and its relevance for multiorbital models

Gang Li, Werner R. Hanke

Published Mar 6, 2012• 4 citations
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Abstract

In this paper, we present an efficient and stable method to determine the one-particle Green's function in the hybridization-expansion continuous-time (CT-HYB) quantum Monte Carlo method within the framework of the dynamical mean-field theory. The high-frequency tail of the impurity self-energy is replaced with a noise-free function determined by a dual-expansion around the atomic limit. This method does not depend on the explicit form of the interaction term. More advantageous, it does not introduce any additional numerical cost to the CT-HYB simulation. We discuss the symmetries of the two-particle vertex, which can be used to optimize the simulation of the four-point correlation functions in the CT-HYB. Here, we adopt it to accelerate the dual-expansion calculation, which turns out to be especially suitable for the study of material systems with complicated band structures. As an application, a two-orbital Anderson impurity model with a general on-site interaction form is studied. The phase diagram is extracted as a function of the Coulomb interactions for two different Hund's coupling strengths. In the presence of the hybridization between different orbitals, for smaller interaction strengths, this model shows a transition from metal to band-insulator. Increasing the interaction strengths, this transition is replaced by a crossover from Mott-insulator to band-insulator behavior.

DOI
10.1103/physrevb.85.115103

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In this paper, we present an efficient and stable method to determine the one-particle Green's function in the hybridization-expansion continuous-time (CT-HYB) quantum Monte Carlo method within the framework of the dynamical mean-field theory. The high-frequency tail of the impurity self-energy is replaced with a noise-free function determined by a dual-expansion around the atomic limit. This method does not depend on the explicit form of the interaction term. More advantageous, it does not introduce any additional numerical cost to the CT-HYB simulation. We discuss the symmetries of the two-particle vertex, which can be used to optimize the simulation of the four-point correlation functions in the CT-HYB. Here, we adopt it to accelerate the dual-expansion calculation, which turns out to be especially suitable for the study of material systems with complicated band structures. As an application, a two-orbital Anderson impurity model with a general on-site interaction form is studied. The phase diagram is extracted as a function of the Coulomb interactions for two different Hund's coupling strengths. In the presence of the hybridization between different orbitals, for smaller interaction strengths, this model shows a transition from metal to band-insulator. Increasing the interaction strengths, this transition is replaced by a crossover from Mott-insulator to band-insulator behavior.
We propose efficient measurement procedures for the self-energy and vertex function of the Anderson impurity model within the hybridization expansion continuous-time quantum Monte Carlo algorithm. The method is based on the measurement of higher-order correlation functions related to the quantities being sought through the equation of motion, a technique previously introduced in the numerical renormalization-group context. For the case of interactions of density-density type, the additional correlators can be obtained at essentially no additional computational cost. In combination with a recently introduced method for filtering the Monte Carlo noise using a representation in terms of orthogonal polynomials, we obtain data with unprecedented accuracy. This leads to an enhanced stability in analytical continuations of the self-energy or in two-particle-based theories such as the dual fermion approach. As an illustration of the method we reexamine the previously reported spin-freezing and high-spin to low-spin transitions in a two-orbital model with density-density interactions. In both cases, the vertex function undergoes significant changes, which suggests significant corrections to the dynamical mean-field solutions in dual fermion calculations.
We present a worm sampling method for calculating one- and two-particle Green's functions using continuous-time quantum Monte Carlo simulations in the hybridization expansion (CT-HYB). Instead of measuring Green's functions by removing hybridization lines from partition function configurations, as in conventional CT-HYB, the worm algorithm directly samples the Green's function. We show that worm sampling is necessary to obtain general two-particle Green's functions which are not of density-density type and that it improves the sampling efficiency when approaching the atomic limit. Such two-particle Green's functions are needed to compute off-diagonal elements of susceptibilities and occur in diagrammatic extensions of the dynamical mean-field theory and in efficient estimators for the single-particle self-energy.
Optimized measurements for the susceptibility, self-energy, as well as three-leg and four-leg vertex functions are introduced for the continuous-time hybridization-expansion quantum Monte Carlo solver for the impurity model in the presence of a retarded interaction. The self-energy and vertex functions are computed from impurity averages which involve time integrals over the retarded interaction. They can be evaluated efficiently within the segment representation. These quantities are computed within dynamical mean-field theory in the presence of plasmonic screening. In the antiadiabatic regime, the self-energy is strongly renormalized but retains features of the low energy scale set by the screened interaction. An explicit expression for its high-frequency behavior is provided. Across the screening driven and interaction driven metal-insulator transitions, the vertex functions are found to exhibit similar structural changes, which are hence identified as generic features of the Mott transition.
In this work we introduce a modified real-time continuous-time hybridization-expansion quantum Monte Carlo solver for a time-dependent single-orbital Anderson impurity model: CT-1/2-HYB-QMC. In the proposed method the diagrammatic expansion is performed only for one out of the two spin channels, while the resulting effective single-particle problem for the other spin is solved semi-analytically for each expansion diagram. CT-1/2-HYB-QMC alleviates the dynamical sign problem by reducing the order of sampled diagrams and makes it possible to reach twice as long time scales in comparison to the standard CT-HYB method. We illustrate the new solver by calculating an electric current through impurity in paramagnetic and spin-polarized cases.
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 derive the equations for calculating the high-frequency asymptotics of the local two-particle vertex function for a multiorbital impurity model. These relate the asymptotics for a general local interaction to equal-time two-particle Green's functions, which we sample using continuous-time quantum Monte Carlo simulations with a worm algorithm. As specific examples we study the single-orbital Hubbard model and the three t2g{t}_{2g}t2g​ orbitals of SrVO3{\mathrm{SrVO}}_{3}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 nonlocal susceptibilities in DMFT and diagrammatic extensions of DMFT.