Real-frequency Diagrammatic Monte Carlo at Finite Temperature

Abstract

Diagrammatic expansions are a central tool for treating correlated electron systems. At thermal equilibrium, they are most naturally defined within the Matsubara formalism. However, extracting any dynamic response function from a Matsubara calculation ultimately requires the ill-defined analytical continuation from the imaginary- to the real-frequency domain. It was recently proposed [Phys. Rev. B 99, 035120 (2019)] that the internal Matsubara summations of any interaction-expansion diagram can be performed analytically by using symbolic algebra algorithms. The result of the summations is then an analytical function of the complex frequency rather than Matsubara frequency. Here we apply this principle and develop a diagrammatic Monte Carlo technique which yields results directly on the real-frequency axis. We present results for the self-energy $\Sigma (\omega )$ of the doped 32x32 cyclic square-lattice Hubbard model in a non-trivial parameter regime, where signatures of the pseudogap appear close to the antinode. We discuss the behavior of the perturbation series on the real-frequency axis and in particular show that one must be very careful when using the maximum entropy method on truncated perturbation series. Our approach holds great promise for future application in cases when analytical continuation is difficult and moderate-order perturbation theory may be sufficient to converge the result.

arXiv comment17 pages, 9 figures

References in corpus (42)

• Continuous-time Monte Carlo methods for quantum impurity models
• A continuous-time solver for quantum impurity models
• Nonequilibrium dynamical mean-field theory and its applications
• Continuous Time Quantum Monte Carlo method for fermions
• TRIQS: A Toolbox for Research on Interacting Quantum Systems
• Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models
• Polaron Problem by Diagrammatic Quantum Monte Carlo
• Bad metallic transport in a cold atom Fermi-Hubbard system
• Energy resolution and discretization artefacts in the numerical renormalization group
• Continuous-time auxiliary field Monte Carlo for quantum impurity models
• A New Iterative Perturbation Scheme for Lattice Models with Arbitrary Filling
• Taming the dynamical sign problem in real-time evolution of quantum many-body problems
• Numerical Linked-Cluster Approach to Quantum Lattice Models
• Diagrammatic Monte Carlo
• Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
• Controlling Feynman diagrammatic expansions: physical nature of the pseudo gap in the two-dimensional Hubbard model
• Quantum Critical Transport Near the Mott Transition
• Strange metallicity in the doped Hubbard model
• Determinant Diagrammatic Monte Carlo in the Thermodynamic Limit
• Green's functions from real-time bold-line Monte Carlo: spectral properties of the nonequilibrium Anderson impurity model
• Finite temperature crossovers and the quantum Widom line near the Mott transition
• Continuous Time Quantum Monte Carlo Method for Fermions: Beyond Auxiliary Field Framework
• Extended crossover from Fermi liquid to quasi-antiferromagnet in the half-filled 2D Hubbard model
• Implementation of the Maximum Entropy Method for Analytic Continuation
• Bad-metal behavior reveals Mott quantum criticality in doped Hubbard models
• Quantum Monte-Carlo for correlated out-of-equilibrium nanoelectronics devices
• Conductivity in the square lattice Hubbard model at high temperatures: importance of vertex corrections
• Interpolating self-energy of the infinite-dimensional Hubbard model: Modifying the iterative perturbation theory
• Green's functions from real-time bold-line Monte Carlo
• Reconstructing non-equilibrium regimes of quantum many-body systems from the analytical structure of perturbative expansions
• Angle-resolved photoemission spectroscopy of a Fermi-Hubbard system
• Determinant Monte Carlo for irreducible Feynman diagrams in the strongly correlated regime
• Algorithmic Matsubara Integration for Hubbard-like models
• Determinant Monte Carlo algorithms for dynamical quantities in fermionic systems
• A Quantum Monte Carlo algorithm for out-of-equilibrium Green's functions at long times
• Bad-Metallic Behavior of Doped Mott Insulators
• Quasiparticle Properties of the Superconducting State of the Two Dimensional Hubbard Model
• Inclusion-Exclusion Principle for Many-Body Diagrammatics
• Two-particle correlations in a dynamic cluster approximation with continuous momentum dependence: Superconductivity in the 2D Hubbard model
• A multi-orbital iterated perturbation theory for model Hamiltonians and real material-specific calculations of correlated systems
• Cancellation of vacuum diagrams and long-time limit in out-of-equilibrium diagrammatic Quantum Monte Carlo
• Truncated-Determinant Diagrammatic Monte Carlo for Fermions with Contact Interaction

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• Dynamic Response of an Electron Gas: Towards the Exact Exchange-Correlation Kernel
• Renormalized perturbation theory at large expansion orders
• Algorithmic approach to diagrammatic expansions for real-frequency evaluation of susceptibility functions
• Exchange-correlation effect in the charge response of a warm dense electron gas
• Homotopic Action: A Pathway to Convergent Diagrammatic Theories
• Numerically Exact Generalized Green's Function Cluster Expansions for Electron-Phonon Problems
• Analytical solution for time-integrals in diagrammatic expansions: application to real-frequency diagrammatic Monte Carlo
• Electrical conductivity in the Hubbard model: orbital effects of magnetic field
• Efficient One-Loop-Renormalized Vertex Expansions with Connected Determinant Diagrammatic Monte Carlo
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• Towards numerically exact computation of conductivity in the thermodynamic limit of interacting lattice models
• Combinatorial summation of Feynman diagrams: Equation of state of the 2D SU(N) Hubbard model
• The Weak, the Strong and the Long Correlation Regimes of the Two-Dimensional Hubbard Model at Finite Temperature
• Photoemission "experiments" on holographic lattices
• Strange metallicity in an antiferromagnetic quantum critical model: A sign-problem-free quantum Monte-Carlo study
• Solving the Bethe-Salpeter Equation in Real Frequencies at Finite Temperature
• Fermionic Sign Structure of High-order Feynman diagrams in a Many-fermion System
• Many-body perturbation expansions without diagrams. I. Normal states
• Computation Kernel for Feynman Diagrams
• Majorana Diagrammatics for Quantum Spin-1/2 Models
• Automated evaluation of imaginary time strong coupling diagrams by sum-of-exponentials hybridization fitting