On the Magnetic Structure of Density Matrices

TL;DR

This paper presents a method to analyze the magnetic structure of one-particle density matrices to determine spin configurations and symmetry properties in single determinant wave functions.

Contribution

It introduces a simple test based on the density matrix to classify spin magnetization as collinear, coplanar, or noncoplanar, and relates noncoplanar magnetism to symmetry breaking.

Findings

Density matrix analysis distinguishes spin configurations.

Noncoplanar magnetism links to complex conjugation symmetry breaking.

Classification of wave function symmetry breaking based on density matrices.

Abstract

The spin structure of wave functions is reflected in the magnetic structure of the one-particle density matrix. Indeed, for single determinants we can use either one to determine the other. In this work we discuss how one can simply examine the one-particle density matrix to faithfully determine whether the spin magnetization density vector field is collinear, coplanar, or noncoplanar. For single determinants, this test suffices to distinguish collinear determinants which are eigenfunctions of $\hat{S}_{\hat{n}}$ from noncollinear determinants which are not. We also point out the close relationship between noncoplanar magnetism on the one hand and complex conjugation symmetry breaking on the other. Finally, we use these ideas to classify the various ways single determinant wave functions break and respect symmetries of the Hamiltonian in terms of their one-particle density matrix.