Ultraviolet extrapolations in finite oscillator bases

TL;DR

This paper explores how finite harmonic oscillator bases introduce IR and UV errors in many-body calculations, proposing duality-based methods to improve extrapolation accuracy for both effects.

Contribution

It demonstrates that UV effects can be modeled by a momentum cutoff dual to the IR boundary, extending previous IR-focused approaches to include UV corrections for realistic potentials.

Findings

UV energy corrections depend on potential details

IR corrections depend only on the S-matrix

Controlled extrapolation methods are discussed for larger systems

Abstract

The use of finite harmonic oscillator spaces in many-body calculations introduces both infrared (IR) and ultraviolet (UV) errors. The IR effects are well approximated by imposing a hard-wall boundary condition at a properly identified radius L_eff. We show that duality of the oscillator implies that the UV effects are equally well described by imposing a sharp momentum cutoff at a momentum Lambda_eff complementary to L_eff. By considering two-body systems with separable potentials, we show that the UV energy corrections depend on details of the potential, in contrast to the IR energy corrections, which depend only on the S-matrix. An adaptation of the separable treatment to more general interactions is developed and applied to model potentials as well as to the deuteron with realistic potentials. The previous success with a simple phenomenological form for the UV error is also explained. Possibilities for controlled extrapolations for A > 2 based on scaling arguments are discussed.