Exact emulation of few-body systems at low cost

TL;DR

This paper introduces a novel low-cost method for exactly emulating few-body systems across various physics domains, significantly reducing computational costs while maintaining high accuracy for different parameters.

Contribution

It proves that low-rank Hamiltonian updates allow exact reduction of the A-body problem to low-dimensional equations, enabling efficient emulators for complex quantum systems.

Findings

Exact emulators for few-body scattering and bound states

Emulators maintain accuracy far from snapshot regions

Method applicable to diverse interactions and particle numbers

Abstract

Effective field theories have established themselves as key pillars of modern nuclear physics. They enable a quantitative understanding of the strong nuclear force, provided low-energy constants that parametrize short-distance physics can be determined from experimental data. This, however, often becomes prohibitively expensive due to a significant computational cost of solving the A-body problem. The computational challenge is particularly severe for three-body forces, which are at the frontier of nuclear and atomic physics and play an important role in the equation of state of neutron stars. Here we prove that for a parametric low-rank update of a Hamiltonian, the A-body problem at a fixed energy exactly reduces to a low-dimensional matrix equation regardless of the size of the Hilbert space. As a proof-of-principle, we present exact and computationally cheap snapshot-based emulators for few-body scattering and bound states. Unlike alternatives, our emulators can be used far away from the snapshot region without loss of precision and yield accurate results for parameter values not accessible using conventional solution techniques. Our approach is not restricted by the interaction type, number of particles, and methods for generating snapshots and can be applied to mitigate the computational burden of the A-body problem to a broad class of problems in nuclear, atomic, and molecular physics.