Resummation of diagrammatic series with zero convergence radius for strongly correlated fermions

Abstract

We demonstrate that summing up series of Feynman diagrams can yield unbiased accurate results for strongly-correlated fermions even when the convergence radius vanishes. We consider the unitary Fermi gas, a model of non-relativistic fermions in three-dimensional continuous space. Diagrams are built from partially-dressed or fully-dressed propagators of single particles and pairs. The series is resummed by a conformal-Borel transformation that incorporates the large-order behavior and the analytic structure in the Borel plane, which are found by the instanton approach. We report highly accurate numerical results for the equation of state in the normal unpolarized regime, and reconcile experimental data with the theoretically conjectured fourth virial coefficient.

References in corpus (39)

• Theory of ultracold Fermi gases
• New Measurement of the Electron Magnetic Moment and the Fine Structure Constant
• Critical Exponents of the N-vector model
• Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas
• Exploring the Thermodynamics of a Universal Fermi Gas
• New determination of the fine structure constant and test of the quantum electrodynamics
• The Unitary Fermi Gas: From Monte Carlo to Density Functionals
• Universal Thermodynamics of Degenerate Quantum Gases in the Unitarity Limit
• Ultrafast many-body interferometry of impurities coupled to a Fermi sea
• Thermodynamics of the BCS-BEC crossover
• A Mixture of Bose and Fermi Superfluids
• The BCS-BEC crossover: From ultra-cold Fermi gases to nuclear systems
• Feynman diagrams versus Fermi-gas Feynman emulator
• Virial expansion for a strongly correlated Fermi gas
• Diagrammatic Monte Carlo
• Josephson effect in fermionic superfluids across the BEC-BCS crossover
• High temperature expansion applied to fermions near Feshbach resonance
• Diagrammatic Monte Carlo for Correlated Fermions
• Controlling Feynman diagrammatic expansions: physical nature of the pseudo gap in the two-dimensional Hubbard model
• Connecting strongly correlated superfluids by a quantum point contact
• New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
• From Planar Solitons to Vortex Rings and Lines: Cascade of Solitonic Excitations in a Superfluid Fermi Gas
• Emergent BCS regime of the two-dimensional fermionic Hubbard model: ground-state phase diagram
• Diagrammatic Monte Carlo method for many-polaron problems
• Bold Diagrammatic Monte Carlo Method Applied to Fermionized Frustrated Spins
• Quantum Monte Carlo approaches to nuclear and atomic physics
• Shifted-Action Expansion and Applicability of Dressed Diagrammatic Schemes
• Compelling evidence of renormalons in QCD from high order perturbative expansions
• Spin-Ice State of the Quantum Heisenberg Antiferromagnet on the Pyrochlore Lattice
• Polynomial complexity despite the fermionic sign
• Stability of Dirac Liquids with Strong Coulomb Interaction
• Fermi liquid behavior in the 2D Hubbard model at low temperatures
• Rigorous construction of ground state correlations in graphene: renormalization of the velocities and Ward Identities
• Path integral Monte Carlo determination of the fourth-order virial coefficient for unitary two-component Fermi gas with zero-range interactions
• Automated Calculation Scheme for alpha^n Contributions of QED to Lepton g-2: New Treatment of Infrared Divergence for Diagrams without Lepton Loops
• p-wave Superfluidity by Spin-Nematic Fermi Surface Deformation
• The third virial coefficient of a two-component unitary Fermi gas across an Efimov-effect threshold
• The interaction-sensitive states of a trapped two-component ideal Fermi gas and application to the virial expansion of the unitary Fermi gas
• Interacting Weyl semimetals on a lattice

Cited by in corpus (38)

• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Observation of a smooth polaron-molecule transition in a degenerate Fermi gas
• Physical Resurgent Extrapolation
• Reconstructing non-equilibrium regimes of quantum many-body systems from the analytical structure of perturbative expansions
• Contact and Momentum Distribution of the Unitary Fermi Gas
• Uniformization and Constructive Analytic Continuation of Taylor Series
• $\lambda {\varphi }^4$ Theory II: The Broken Phase Beyond NNNN(NNNN)LO
• Optimal grouping of arbitrary diagrammatic expansions via analytic pole structure
• High-precision numerical solution of the Fermi polaron problem and large-order behavior of its diagrammatic series
• Exchange-correlation effect in the charge response of a warm dense electron gas
• Diagrammatic Monte Carlo algorithm for the resonant Fermi gas
• Conformal and Uniformizing Maps in Borel Analysis
• Resurgence for superconductors
• Exact perturbative results for the Lieb-Liniger and Gaudin-Yang models
• Homotopic Action: A Pathway to Convergent Diagrammatic Theories
• Uniformizing Lee-Yang Singularities
• Effective field theory for dilute Fermi systems at fourth order
• Diagrammatic Monte Carlo Method for Impurity Models with General Interactions and Hybridizations
• The virial expansion of attractively interacting Fermi gases in 1D, 2D, and 3D, up to fifth order
• Cross-extrapolation reconstruction of low-rank functions and application to quantum many-body observables in the strong coupling regime
• Interaction expansion inchworm Monte Carlo solver for lattice and impurity models
• Fast Principal Minor Algorithms for Quantum Many Body Systems
• Zero-temperature limit and statistical quasiparticles in many-body perturbation theory
• Fourth- and fifth-order virial expansion of harmonically trapped fermions at unitarity
• From weak to strong: constrained extrapolation of perturbation series with applications to dilute Fermi systems
• Spectral functions of the strongly interacting 3D Fermi gas
• A Multi-Purpose Platform for Analog Quantum Simulation
• Three-body contact for fermions. I. General relations
• Feynman's solution of the quintessential problem in solid state physics
• Physical and unphysical regimes of self-consistent many-body perturbation theory
• Constrained extrapolation problem and order-dependent mappings
• Fermionic Sign Structure of High-order Feynman diagrams in a Many-fermion System
• All electron GW with linearized augmented plane waves for metals and semiconductors
• Matsubara-Frequency-Resolved Spin Exchange-Correlation Kernel for the Three-Dimensional Uniform Electron Gas
• Fourth cluster and virial coefficients of a unitary Fermi gas for an arbitrary mass ratio
• Universality, Lee-Yang singularities and series expansions
• Diagrammatic Monte Carlo for Finite Systems at Zero Temperature
• Local energy density functional for superfluid Fermi gases from effective field theory