Artificial Symmetry Breaking by Self-Interaction Error

TL;DR

This paper demonstrates that self-interaction error in density functional theory can cause artificial symmetry breaking, affecting the interpretation of electronic states in materials, and proposes a functional to mitigate this issue.

Contribution

It provides clear evidence that self-interaction error alone can induce artificial symmetry breaking and introduces a new functional to avoid this artifact.

Findings

Self-interaction error causes symmetry breaking in one-electron systems.

A new semilocal functional avoids artificial symmetry breaking.

Real-world defect in ZnO exhibits symmetry breaking due to SIE.

Abstract

Symmetry is a cornerstone of quantum mechanics and materials theory, underpinning the classification of electronic states and the emergence of complex phenomena such as magnetism and superconductivity. While symmetry breaking in density functional theory can reveal strong electron correlation, it may also arise spuriously from self-interaction error (SIE), an intrinsic flaw in many approximate exchange-correlation functionals. In this work, we present clear evidence that SIE alone can induce artificial symmetry breaking, even in the absence of strong correlation. Using a family of one-electron, multi-nuclear-center systems \( \mathrm{H}^+_{n \times \frac{+2}{n}}(R) \), we show that typical semilocal density functionals exhibit symmetry-breaking localization as system size increases, deviating from the exact, symmetry-preserving Hartree-Fock solution. We further demonstrate that this localization error contrasts with the well-known delocalization error of semilocal density functionals and design a semilocal density functional that avoids the artifact. Finally, we illustrate the real-world relevance of this effect in the \ch{Ti_{Zn}v_O} defect in ZnO, where a semilocal density functional breaks the $C_{3v}$ symmetry while a hybrid density functional preserves it. These findings highlight the need for improved functional design to prevent spurious symmetry breaking in both model and real materials.