Constrained Extrapolation Problem and Order‐Dependent Mappings. Issue 9 (15th April 2021)

• Record Type: Journal Article
• Authors: Wellenhofer, Corbinian; Phillips, Daniel R.; Schwenk, Achim
• Is Part Of: Physica status solidi. Volume 258:Issue 9(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-04-15
• Subjects: dilute Fermi gas -- resummation of perturbation series -- maximum-entropy method -- strongly correlated systems; Solid state physics -- Periodicals; Solids -- Periodicals; Atomic structure -- Periodicals; 530.41
• DOI: 10.1002/pssb.202000554
• Languages: English
• ISSNs: 0370-1972

Abstract

Abstract : 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 is considered, 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, it is shown that the 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 (MaxEnt) extrapolation method. However, it is shown 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, order‐dependent‐mapping extrapolation (ODME) as a simple, practical, and general method for the CEP is proposed. It is found 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. Abstract : This work surveys different approaches for extrapolating a perturbation series from weak to strong coupling using low‐order constraints from the strong‐coupling regime. It is shown that the recently developed order‐dependent‐mapping extrapolation (ODME) often performs better than standard methods, such as Padé and Borel resummation. ODME also compares favorably to the more general maximum‐entropy (MaxEnt) extrapolation technique.