Importance truncation for the in-medium similarity renormalization group

TL;DR

This paper introduces importance truncation techniques to reduce computational costs in the in-medium similarity renormalization group method for nuclear many-body problems, maintaining accuracy while significantly compressing the problem size.

Contribution

It applies importance-truncation to IMSRG, identifies effective importance measures, and demonstrates minimal errors with high compression ratios across various nuclei.

Findings

Best importance measures identified for minimal errors

Small errors maintained with high compression ratios

Effective for soft Hamiltonians and large bases

Abstract

Ab initio nuclear many-body frameworks require extensive computational resources, especially when targeting heavier nuclei. Importance-truncation (IT) techniques allow to significantly reduce the dimensionality of the problem by neglecting unimportant contributions to the solution of the many-body problem. In this work, we apply IT methods to the nonperturbative in-medium similarity renormalization group (IMSRG) approach and investigate the induced errors for ground-state energies in different mass regimes based on different nuclear Hamiltonians. We study various importance measures, which define the IT selection, and identify two measures that perform best, resulting in only small errors to the full IMSRG(2) calculations even for sizable compression ratios. The neglected contributions are accounted for in a perturbative way and serve as an estimate of the IT-induced error. Overall we find that the IT-IMSRG(2) performs well across all systems considered, while the largest compression ratios for a given error can be achieved when using soft Hamiltonians and for large single-particle bases.