Continuous-time quantum Monte Carlo calculation of multi-orbital vertex asymptotics

Abstract

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 continuous-time quantum Monte Carlo simulations with a worm algorithm. As specific examples we study the single-orbital Hubbard model and the three $t_{2g}$ orbitals of SrVO${}_3$ 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.

14 pages, 12 figures

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• Fingerprints of the local moment formation and its Kondo screening in the generalized susceptibilities of many-electron problems
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• Magnetic response of Sr${}_2$RuO${}_4$: quasi-local spin fluctuations due to Hund's coupling
• Boson-Exchange Parquet Solver for dual fermions
• Sparse Modeling in Quantum Many-Body Problems
• Interplay between local response and vertex divergences in many-fermion systems with on-site attraction
• Overcomplete compact representation of two-particle Green's functions
• Self-consistent ladder D$\Gamma$A approach
• Efficient Bethe-Salpeter equations' treatment in dynamical mean-field theory
• Symmetric Improved Estimators for Continuous-time Quantum Monte Carlo
• Quantum criticality in the two-dimensional periodic Anderson model
• Role of three-particle vertex within dual fermion calculations
• Efficient evaluation of the polarization function in dynamical mean-field theory
• Sparse sampling and tensor network representation of two-particle Green's functions
• Fermi liquid theory and divergences of the two-particle irreducible vertex in the periodic Anderson lattice
• Parquet approximation for molecules: spectrum and optical conductivity of the Pariser-Parr-Pople model
• Towards ab initio calculations with the dynamical vertex approximation
• The AbinitioD$\Gamma$A Project v1.0: Non-local correlations beyond and susceptibilities within dynamical mean-field theory
• Accelerated impurity solver for DMFT and its diagrammatic extensions
• Symmetric improved estimators for multipoint vertex functions
• Statistical error estimates in dynamical mean-field theory and extensions thereof
• Dual Bethe-Salpeter equation for the multi-orbital lattice susceptibility within dynamical mean-field theory
• Development of an efficient impurity solver in dynamical mean field theory for multi-band systems: The iterative perturbation theory combined with the parquet equations
• Interplay between nematic fluctuation and superconductivity in the two-orbital Hubbard model: A quantum Monte Carlo study
• Simplification of the local full vertex in the impurity problem in DMFT and its applications for the nonlocal correlation
• Computing local multipoint correlators using the numerical renormalization group
• Improvement of the simplification method for the local two-particle full-vertex towards precise frequency behavior
• Multi-band D-TRILEX approach to materials with strong electronic correlations
• Strong-coupling formula for momentum-dependent susceptibilities in dynamical mean-field theory