Geometry of effective Hamiltonians

TL;DR

This paper provides a comprehensive geometric framework for understanding effective Hamiltonians in nuclear shell models, clarifying key concepts, introducing new insights, and proposing improved numerical algorithms.

Contribution

It offers a novel geometric formulation of effective Hamiltonians, clarifies the role of symmetries, and introduces algorithms to enhance computational stability.

Findings

Complete geometric description of effective Hamiltonians

New insights into commuting observables and symmetries

Algorithms for improved numerical stability

Abstract

We give a complete geometrical description of the effective Hamiltonians common in nuclear shell model calculations. By recasting the theory in a manifestly geometric form, we reinterpret and clarify several points. Some of these results are hitherto unknown or unpublished. In particular, commuting observables and symmetries are discussed in detail. Simple and explicit proofs are given, and numerical algorithms are proposed, that improve and stabilize common methods used today.