Operator evolution from the similarity renormalization group and the Magnus expansion

TL;DR

This paper explores the use of the Magnus expansion as an efficient method for operator evolution within the similarity renormalization group framework, demonstrating its effectiveness in nuclear physics applications and addressing scale dependence issues.

Contribution

It introduces the Magnus expansion as a practical alternative for SRG operator evolution, especially in complex nuclear physics problems involving high cutoffs and scheme dependence.

Findings

Magnus expansion successfully handles SRG operator evolution in challenging scenarios.

The approach reveals insights into universality and scheme dependence of nuclear operators.

Implications for nuclear structure and reactions at different scales are discussed.

Abstract

The Magnus expansion is an efficient alternative to solving similarity renormalization group (SRG) flow equations with high-order, memory-intensive ordinary differential equation solvers. The numerical simplifications it offers for operator evolution are particularly valuable for in-medium SRG calculations, though challenges remain for difficult problems involving intruder states. Here we test the Magnus approach in an analogous but more accessible situation, which is the free-space SRG treatment of the spurious bound-states arising from a leading-order chiral effective field theory (EFT) potential with very high cutoffs. We show that the Magnus expansion passes these tests and then use the investigations as a springboard to address various aspects of operator evolution that have renewed relevance in the context of the scale and scheme dependence of nuclear processes. These aspects include SRG operator flow with band- versus block-diagonal generators, universality for chiral EFT Hamiltonians and associated operators with different regularization schemes, and the impact of factorization arising from scale separation. Implications for short-range correlations physics and the possibilities for reconciling high- and low-resolution treatments of nuclear structure and reactions are discussed.