From weak to strong: constrained extrapolation of perturbation series with applications to dilute Fermi systems

Abstract

We develop a method that uses truncation-order-dependent re-expansions constrained by generic strong-coupling information to extrapolate perturbation series to the nonperturbative regime. The method is first benchmarked against a zero-dimensional model field theory and then applied to the dilute Fermi gas in one and three dimensions. Overall, our method significantly outperforms Padé and Borel extrapolations in these examples. The results for the ground-state energy of the three-dimensional Fermi gas are robust with respect to changes of the form of the re-expansion and compare well with quantum Monte Carlo simulations throughout the BCS regime and beyond.

arXiv commentminor improvements, matches published version; 11 pages, 8 figures

References in corpus (36)

• Many-Body Physics with Ultracold Gases
• Feshbach Resonances in Ultracold Gases
• Theory of ultracold Fermi gases
• Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas
• Fermi gases in one dimension: From Bethe Ansatz to experiments
• Symmetry Parameter Constraints From A Lower Bound On The Neutron-Matter Energy
• Resonant Fermi gases with a large effective range
• An exactly solvable model of the BCS-BEC crossover
• Neutron Matter from Low to High Density
• Auxiliary Field quantum Monte Carlo for Strongly Paired Fermions
• BEC-BCS crossover and universal relations in unitary Fermi gases
• Improved Convergence Proof of the Delta Expansion and Order Dependent Mappings
• Convergence of the Optimized Delta Expansion for the Connected Vacuum Amplitude: Zero Dimensions
• Resummation of diagrammatic series with zero convergence radius for strongly correlated fermions
• Convergent resummed linear delta expansion in the critical O(N) (ϕ_i^2)^2_{3d} model
• Resummation of fermionic in-medium ladder diagrams to all orders
• Resurgent Extrapolation: Rebuilding a Function from Asymptotic Data. Painleve I
• Convergence of the Linear Delta Expansion in the Critical O(N) Field Theory
• Variational Interpolation Algorithm between Weak- and Strong-Coupling Expansions
• Convergent sequences of perturbative approximations for the anharmonic oscillator I. Harmonic approach
• One-dimensional multicomponent fermions with delta function interaction in strong and weak coupling limits: Two-component Fermi gas
• Resurgence and Holomorphy: From Weak to Strong Coupling
• On the Divergence of Perturbation Theory. Steps Towards a Convergent Series
• Higher-order perturbative coefficients in QCD from series acceleration by conformal mappings
• Resurgence for superconductors
• Exact perturbative results for the Lieb-Liniger and Gaudin-Yang models
• New Optimization Methods for Converging Perturbative Series with a Field Cutoff
• On Perturbation theory improved by Strong coupling expansion
• Dilute Fermi gas at fourth order in effective field theory
• The fourth- and fifth-order virial coefficients from weak-coupling to unitarity
• Interpolating function and Stokes Phenomena
• Zero-temperature limit and statistical quasiparticles in many-body perturbation theory
• Approximate self-energy for Fermi systems with large s-wave scattering length: a step towards density functional theory
• Variational Perturbation Theory for Summing Divergent Non-Borel-Summable Tunneling Amplitudes
• Summing Non-Borel Tunnelling Amplitudes by Variational Perturbation Theory
• Distribution of solutions of the fastest apparent convergence condition in optimized perturbation theory and its relation to anti-Stokes lines

Cited by in corpus (6)

• Effective field theory for dilute Fermi systems at fourth order
• Quantum Monte Carlo simulations of two-dimensional repulsive Fermi gases with population imbalance
• Interpolating between small- and large-$g$ expansions using Bayesian Model Mixing
• Bayesian inference of neutron star crust properties using an ab initio-benchmarked meta-model
• Constrained extrapolation problem and order-dependent mappings
• Toward precision Fermi liquid theory in two dimensions