Constrained extrapolation problem and order-dependent mappings
arXiv:2011.02105 · doi:10.1002/pssb.202000554
Abstract
We consider the problem of extrapolating the perturbation series for the dilute Fermi gas in three dimensions to the unitary limit of infinite scattering length and into the BEC region, using the available strong-coupling information to constrain the extrapolation problem. In this constrained extrapolation problem (CEP) the goal is to find classes of approximants that give well converged results already for low perturbative truncation orders. First, we show that standard Padé and Borel methods are too restrictive to give satisfactory results for this CEP. A generalization of Borel extrapolation is given by the so-called Maximum Entropy extrapolation method (MaxEnt). However, we show that MaxEnt requires extensive elaborations to be applicable to the dilute Fermi gas and is thus not practical for the CEP in this case. Instead, we propose order-dependent-mapping extrapolation (ODME) as a simple, practical, and general method for the CEP. We find that the ODME approximants for the ground-state energy of the dilute Fermi gas are robust with respect to changes of the mapping choice and agree with results from quantum Monte Carlo simulations within uncertainties.
arXiv comment19 pages, 3 figures. Paper prepared for the Festschrift in honor of the 60th birthday of Prof. D.A. Drabold. This version has minor changes in response to referee comments. Almost identical to version published in Physica Status Solidi B: Basic Solid State Physics
References in corpus (37)
- 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
- The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions
- Symmetry Parameter Constraints From A Lower Bound On The Neutron-Matter Energy
- A Primer on Resurgent Transseries and Their Asymptotics
- An Introduction to Resurgence, Trans-Series and Alien Calculus
- Variational perturbation expansion for strong-coupling coefficients of the anharmonic oscillator
- Resonant Fermi gases with a large effective range
- Neutron Matter from Low to High Density
- Auxiliary Field quantum Monte Carlo for Strongly Paired Fermions
- Convergence of Scaled Delta Expansion: Anharmonic Oscillator
- New equations of state constrained by nuclear physics, observations, and QCD calculations of high-density nuclear matter
- 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
- Convergence of the Optimized Delta Expansion for the Connected Vacuum Amplitude -- Anharmonic Oscillator
- Variational Interpolation Algorithm between Weak- and Strong-Coupling Expansions
- 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
- Exact perturbative results for the Lieb-Liniger and Gaudin-Yang models
- Resurgence for superconductors
- Dilute Fermi gas at fourth order in effective field theory
- The fourth- and fifth-order virial coefficients from weak-coupling to unitarity
- Dependence of Variational Perturbation Expansions on Strong-Coupling Behavior. Inapplicability of delta-Expansion to Field Theory
- Interplay Between Approximation Theory and Renormalization Group
- Interpolating function and Stokes Phenomena
- Zero-temperature limit and statistical quasiparticles in many-body perturbation theory
- From weak to strong: constrained extrapolation of perturbation series with applications to dilute Fermi systems
- Distribution of solutions of the fastest apparent convergence condition in optimized perturbation theory and its relation to anti-Stokes lines