# Interpretations of ground-state symmetry breaking and strong correlation in wavefunction and density functional theories

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Contributed by John P. Perdew, November 23, 2020 (sent for review August 24, 2020; reviewed by Neepa Maitra and Giovanni Vignale)

## Significance

The ground state of a quantum mechanical system is the lowest-energy eigenstate of the Hamiltonian. In isolation, it persists unchanged forever, with symmetries dictated by those of the Hamiltonian. But near-eigenstates of broken symmetry can persist for long times, even on the scale of human measurement. The appearance of broken symmetries of the electron density or spin density in a density functional calculation can reveal strong correlations among the electrons that are present in a symmetry-unbroken wavefunction. Symmetry breaking can arise when a wave-like fluctuation drops to zero frequency. The presented examples are the stretched hydrogen molecule, antiferromagnetism in solids, and the static charge-density wave in a low-density jellium, which is shown quantitatively to be a zero-frequency plasma wave.

## Abstract

Strong correlations within a symmetry-unbroken ground-state wavefunction can show up in approximate density functional theory as symmetry-broken spin densities or total densities, which are sometimes observable. They can arise from soft modes of fluctuations (sometimes collective excitations) such as spin-density or charge-density waves at nonzero wavevector. In this sense, an approximate density functional for exchange and correlation that breaks symmetry can be more revealing (albeit less accurate) than an exact functional that does not. The examples discussed here include the stretched H_{2} molecule, antiferromagnetic solids, and the static charge-density wave/Wigner crystal phase of a low-density jellium. Time-dependent density functional theory is used to show quantitatively that the static charge-density wave is a soft plasmon. More precisely, the frequency of a related density fluctuation drops to zero, as found from the frequency moments of the spectral function, calculated from a recent constraint-based wavevector- and frequency-dependent jellium exchange-correlation kernel.

## Footnotes

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^{1}To whom correspondence may be addressed. Email: kaplan{at}temple.edu or perdew{at}temple.edu.

Author contributions: J.P.P., A.R., J.S., N.K.N., and A.D.K. designed research; J.P.P., A.R., and J.S. performed research; N.K.N. and A.D.K. analyzed data; and J.P.P., A.R., and J.S. wrote the paper.

Reviewers: N.M., Rutgers University; and G.V., University of Missouri.

The authors declare no competing interest.

This article contains supporting information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.2017850118/-/DCSupplemental.

## Data Availability.

All relevant data are available within the manuscript and *SI Appendix*. All raw data are publicly available at the Materials Cloud Archive (DOI: 10.24435/materialscloud:vh-wc) (56). The code used was written for this project and is publicly available in GitLab at https://gitlab.com/dhamil/mcp07-kernel-testing.

Published under the PNAS license.

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