Efficient One-Loop-Renormalized Vertex Expansions with Connected Determinant Diagrammatic Monte Carlo

Abstract

We present a technique that enables the evaluation of perturbative expansions based on one-loop-renormalized vertices up to large expansion orders. Specifically, we show how to compute large-order corrections to the random phase approximation in either the particle-hole or particle-particle channels. The algorithm's efficiency is achieved by the summation over contributions of all symmetrized Feynman diagram topologies using determinants, and by integrating out analytically the two-body long-range interactions in order to yield an effective zero-range interaction. Notably, the exponential scaling of the algorithm as a function of perturbation order leads to a polynomial scaling of the approximation error with computational time for a convergent series. To assess the performance of our approach, we apply it to the non-perturbative regime of the square-lattice fermionic Hubbard model away from half-filling and report, as compared to the bare interaction expansion algorithm, significant improvements of the Monte Carlo variance as well as the convergence properties of the resulting perturbative series.

arXiv comment12 pages, 10 figures

References in corpus (40)

• Cold bosonic atoms in optical lattices
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• A Mott insulator of fermionic atoms in an optical lattice
• Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
• Metallic and Insulating Phases of Repulsively Interacting Fermions in a 3D Optical Lattice
• Continuous Time Quantum Monte Carlo method for fermions
• Fermionic atoms in a 3D optical lattice: Observing Fermi-surfaces, dynamics and interactions
• Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
• Observation of Spatial Charge and Spin Correlations in the 2D Fermi-Hubbard Model
• Polaron Problem by Diagrammatic Quantum Monte Carlo
• Site-resolved measurement of the spin-correlation function in the Hubbard model
• Feynman diagrams versus Fermi-gas Feynman emulator
• Diagrammatic Monte Carlo
• Spin Transport in a Mott Insulator of Ultracold Fermions
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• 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
• Doublon-hole correlations and fluctuation thermometry in a Fermi-Hubbard gas
• Extended crossover from Fermi liquid to quasi-antiferromagnet in the half-filled 2D Hubbard model
• Quantum Monte-Carlo for correlated out-of-equilibrium nanoelectronics devices
• Formation and dynamics of anti-ferromagnetic correlations in tunable optical lattices
• Emergent BCS regime of the two-dimensional fermionic Hubbard model: ground-state phase diagram
• Shifted-Action Expansion and Applicability of Dressed Diagrammatic Schemes
• 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
• Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions
• Dynamics of Kondo voltage splitting after a quantum quench
• Algorithmic Matsubara Integration for Hubbard-like models
• Determinant Monte Carlo algorithms for dynamical quantities in fermionic systems
• Polynomial complexity despite the fermionic sign
• Inclusion-Exclusion Principle for Many-Body Diagrammatics
• Real-frequency Diagrammatic Monte Carlo at Finite Temperature
• Optimal grouping of arbitrary diagrammatic expansions via analytic pole structure
• Renormalized perturbation theory at large expansion orders
• 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
• Cancellation of vacuum diagrams and long-time limit in out-of-equilibrium diagrammatic Quantum Monte Carlo
• Direct sampling of the self-energy with Connected Determinant Monte Carlo

Cited by in corpus (7)

• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• Homotopic Action: A Pathway to Convergent Diagrammatic Theories
• Analytical solution for time-integrals in diagrammatic expansions: application to real-frequency diagrammatic Monte Carlo
• Fast Principal Minor Algorithms for Quantum Many Body Systems
• Physical and unphysical regimes of self-consistent many-body perturbation theory
• Evaluating second-order phase transitions with Diagrammatic Monte Carlo: Néel Transition in the doped three-dimensional Hubbard model
• Majorana Diagrammatics for Quantum Spin-1/2 Models