Sparse sampling and tensor network representation of two-particle Green's functions
arXiv:1909.07519 · doi:10.21468/SciPostPhys.8.1.012
Abstract
Many-body calculations at the two-particle level require a compact representation of two-particle Green's functions. In this paper, we introduce a sparse sampling scheme in the Matsubara frequency domain as well as a tensor network representation for two-particle Green's functions. The sparse sampling is based on the intermediate representation basis and allows an accurate extraction of the generalized susceptibility from a reduced set of Matsubara frequencies. The tensor network representation provides a system independent way to compress the information carried by two-particle Green's functions. We demonstrate efficiency of the present scheme for calculations of static and dynamic susceptibilities in single- and two-band Hubbard models in the framework of dynamical mean-field theory.
27 pages in single column format, 12 pages (added missing references)
References in corpus (39)
- The density-matrix renormalization group in the age of matrix product states
- A continuous-time solver for quantum impurity models
- TRIQS: A Toolbox for Research on Interacting Quantum Systems
- Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models
- Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
- Dynamical vertex approximation - a step beyond dynamical mean field theory
- Differentiable Programming Tensor Networks
- TRIQS/DFTTools: A TRIQS application for ab initio calculations of correlated materials
- Local Electronic Correlation at the Two-Particle Level
- Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
- Mott physics and spin fluctuations: a unified framework
- Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs
- From infinite to two dimensions through the functional renormalization group
- Efficient perturbation theory for quantum lattice models
- Updated Core Libraries of the ALPS Project
- Sparse sampling approach to efficient ab initio calculations at finite temperature
- Superconductivity from emerging magnetic moments
- High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
- Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings
- Influence of Spatial Correlations in Strongly Correlated Electron Systems: Extension to Dynamical Mean Field Approximation
- Superconductivity, antiferromagnetism and phase separation in the two-dimensional Hubbard model: A dual-fermion approach
- Efficient implementation of the parquet equations -- role of the reducible vertex function and its kernel approximation
- Ab initio dynamical vertex approximation
- Low rank factorization of the Coulomb integrals for periodic coupled cluster theory
- One-particle irreducible functional approach - a new route to diagrammatic extensions of DMFT
- Efficient treatment of two-particle vertices in dynamical mean-field theory
- Efficient ab initio auxiliary-field quantum Monte Carlo calculations in Gaussian bases via low-rank tensor decomposition
- Mott physics and collective modes: an atomic approximation of the four-particle irreducible functional
- FLEX+DMFT approach to the -wave superconducting phase diagram of the two-dimensional Hubbard model
- Critical Exponents of Strongly Correlated Fermion Systems from Diagrammatic Multi-Scale Methods
- Continuous-time hybridization expansion quantum impurity solver for multi-orbital systems with complex hybridizations
- Sparse Modeling in Quantum Many-Body Problems
- Collective Modes in Excitonic Magnets: Dynamical Mean-Field Study
- irbasis: Open-source database and software for intermediate-representation basis functions of imaginary-time Green's function
- Overcomplete compact representation of two-particle Green's functions
- Continuous-time quantum Monte Carlo calculation of multi-orbital vertex asymptotics
- Phase diagram of exciton condensate in doped two-band Hubbard model
- Hidden physics in the dual-fermion approach - a special case of a non-local expansion scheme
- Updated Core Libraries of the ALPS Project
Cited by in corpus (25)
- Discrete Lehmann representation of imaginary time Green's functions
- sparse-ir: optimal compression and sparse sampling of many-body propagators
- Multiscale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains
- Multipoint correlation functions: spectral representation and numerical evaluation
- Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function
- Solving the Bethe-Salpeter equation with exponential convergence
- Strongly correlated superconductivity with long-range spatial fluctuations
- Two-particle calculations with quantics tensor trains: Solving the parquet equations
- Charge Density Wave Ordering in NdNiO: Effects of Multiorbital Nonlocal Correlations
- DCore: Integrated DMFT software for correlated electrons
- Real-frequency quantum field theory applied to the single-impurity Anderson model
- Dynamical response and competing orders in two-band Hubbard model
- Statistical error estimates in dynamical mean-field theory and extensions thereof
- Multipolar ordering from dynamical mean field theory with application to CeB6
- Discrete Lehmann representation of three-point functions
- Compressing the two-particle Green's function using wavelets: Theory and application to the Hubbard atom
- Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions
- Subleading logarithmic behavior in the parquet formalism
- Simplification of the local full vertex in the impurity problem in DMFT and its applications for the nonlocal correlation
- Entanglement across scales: Quantics tensor trains as a natural framework for renormalization
- Inchworm tensor train hybridization expansion quantum impurity solver
- Broadening and sharpening of the Drude peak through antiferromagnetic fluctuations
- Antiferromagnetic magnons and local anisotropy: dynamical mean-field study
- Improvement of the simplification method for the local two-particle full-vertex towards precise frequency behavior
- Imaginary Time Formalism for Causal Nonlinear Response Functions