Determinant Monte Carlo algorithms for dynamical quantities in fermionic systems

Abstract

We introduce and compare three different Monte Carlo determinantal algorithms that allow one to compute dynamical quantities, such as the self-energy, of fermionic systems in their thermodynamic limit. We show that the most efficient approach expresses the sum of a factorial number of one-particle-irreducible diagrams as a recursive sum of determinants with exponential complexity. By comparing results for the two-dimensional Hubbard model with those obtained from state-of-the-art diagrammatic Monte Carlo, we show that we can reach higher perturbation orders and greater accuracy for the same computational effort.

References in corpus (31)

• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Continuous-time Monte Carlo methods for quantum impurity models
• Quantum Cluster Theories
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• A continuous-time solver for quantum impurity models
• Continuous Time Quantum Monte Carlo method for fermions
• Cellular Dynamical Mean Field Approach to Strongly Correlated Systems
• Nonlocal Dynamical Correlations of Strongly Interacting Electron Systems
• TRIQS: A Toolbox for Research on Interacting Quantum Systems
• Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
• Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models
• Antiferromagnetism and d-wave superconductivity in cuprates: a uster DMFT study
• Polaron Problem by Diagrammatic Quantum Monte Carlo
• Numerical Renormalization Group Calculations for the Self-energy of the impurity Anderson model
• Continuous-time auxiliary field Monte Carlo for quantum impurity models
• Critical Temperature and Thermodynamics of Attractive Fermions at Unitarity
• Feynman diagrams versus Fermi-gas Feynman emulator
• Diagrammatic Monte Carlo
• Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
• Diagrammatic Monte Carlo for Correlated Fermions
• Controlling Feynman diagrammatic expansions: physical nature of the pseudo gap in the two-dimensional Hubbard model
• Determinant Diagrammatic Monte Carlo in the Thermodynamic Limit
• Continuous Time Quantum Monte Carlo Method for Fermions: Beyond Auxiliary Field Framework
• Quantum Monte-Carlo for correlated out-of-equilibrium nanoelectronics devices
• On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime
• Emergent BCS regime of the two-dimensional fermionic Hubbard model: ground-state phase diagram
• Shifted-Action Expansion and Applicability of Dressed Diagrammatic Schemes
• Polynomial complexity despite the fermionic sign
• Ground state phase diagram of the repulsive fermionic $t-t^{\prime }$ Hubbard model on the square lattice from weak-coupling
• Magnetic Correlations in the Two-dimensional Repulsive Fermi Hubbard Model
• Truncated-Determinant Diagrammatic Monte Carlo for Fermions with Contact Interaction

Cited by in corpus (37)

• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• Mott insulating states with competing orders in the triangular lattice Hubbard model
• Extended crossover from Fermi liquid to quasi-antiferromagnet in the half-filled 2D Hubbard model
• Reconstructing non-equilibrium regimes of quantum many-body systems from the analytical structure of perturbative expansions
• Spin and charge correlations across the metal-to-insulator crossover in the half-filled $2d$ Hubbard model
• Determinant Monte Carlo for irreducible Feynman diagrams in the strongly correlated regime
• Impact of partially bosonized collective fluctuations on electronic degrees of freedom
• Algorithmic Matsubara Integration for Hubbard-like models
• A Quantum Monte Carlo algorithm for out-of-equilibrium Green's functions at long times
• Dual Boson Diagrammatic Monte Carlo Approach Applied to the Extended Hubbard Model
• Inclusion-Exclusion Principle for Many-Body Diagrammatics
• Origin and fate of the pseudogap in the doped Hubbard model
• Symmetric Improved Estimators for Continuous-time Quantum Monte Carlo
• Real-frequency Diagrammatic Monte Carlo at Finite Temperature
• A Tensor Train Continuous Time Solver for Quantum Impurity Models
• Optimal grouping of arbitrary diagrammatic expansions via analytic pole structure
• Renormalized perturbation theory at large expansion orders
• Algorithmic approach to diagrammatic expansions for real-frequency evaluation of susceptibility functions
• High-precision numerical solution of the Fermi polaron problem and large-order behavior of its diagrammatic series
• Diagrammatic Monte Carlo algorithm for the resonant Fermi gas
• Exchange-correlation effect in the charge response of a warm dense electron gas
• Real-space cluster dynamical mean-field theory: Center focused extrapolation on the one- and two particle level
• Homotopic Action: A Pathway to Convergent Diagrammatic Theories
• Analytical solution for time-integrals in diagrammatic expansions: application to real-frequency diagrammatic Monte Carlo
• Efficient One-Loop-Renormalized Vertex Expansions with Connected Determinant Diagrammatic Monte Carlo
• Cancellation of vacuum diagrams and long-time limit in out-of-equilibrium diagrammatic Quantum Monte Carlo
• Nonlocal corrections to dynamical mean-field theory from the two-particle self-consistent method
• Diagrammatic Monte Carlo Method for Impurity Models with General Interactions and Hybridizations
• Single particle properties of the 2D Hubbard model for real frequencies at weak coupling: Breakdown of the Dyson series for partial self-energy expansions
• Interaction expansion inchworm Monte Carlo solver for lattice and impurity models
• Decomposing imaginary time Feynman diagrams using separable basis functions: Anderson impurity model strong coupling expansion
• Non-linear responses and three-particle correlators in correlated electron systems exemplified by the Anderson impurity model
• Fermionic Sign Structure of High-order Feynman diagrams in a Many-fermion System
• Physical and unphysical regimes of self-consistent many-body perturbation theory
• Improved estimator for numerical renormalization group calculations of the self-energy
• In-Depth Investigation of Phase Transition Phenomena in Network Models Derived from Lattice Models
• Evaluating second-order phase transitions with Diagrammatic Monte Carlo: Néel Transition in the doped three-dimensional Hubbard model