The Magnus expansion and the in-medium similarity renormalization group

TL;DR

This paper introduces an improved IM-SRG method using the Magnus expansion, enabling efficient unitary transformations and operator evolution with reduced computational resources, demonstrated on electron gas and oxygen-16.

Contribution

The paper develops a Magnus expansion-based formulation of IM-SRG that simplifies computations and allows easy transformation of multiple operators.

Findings

Memory savings and speedups in flow equation solutions.

Accurate ground state calculations for HEG and $^{16}$O.

Efficient transformation of operators beyond the Hamiltonian.

Abstract

We present an improved variant of the in-medium similarity renormalization group (IM-SRG) based on the Magnus expansion. In the new formulation, one solves flow equations for the anti-hermitian operator that, upon exponentiation, yields the unitary transformation of the IM-SRG. The resulting flow equations can be solved using a first-order Euler method without any loss of accuracy, resulting in substantial memory savings and modest computational speedups. Since one obtains the unitary transformation directly, the transformation of additional operators beyond the Hamiltonian can be accomplished with little additional cost, in sharp contrast to the standard formulation of the IM-SRG. Ground state calculations of the homogeneous electron gas (HEG) and $^{16}$O nucleus are used as test beds to illustrate the efficacy of the Magnus expansion.