Symmetry-resolved fermionic correlations in iron-oxide ground spaces
Abstract
Symmetries of quantum systems provide a natural way to organize the eigenspaces of many-body Hamiltonians. When degeneracies exist, however, they play a more subtle role as different sets of symmetry operators can resolve the same energy subspace into states with very different correlation properties. We study this interplay using a sequence of FeO and Fe2O2 models. For a Hubbard model of FeO, the ground space is 16-fold degenerate. Resolving it by local magnetizations gives a basis of Slater determinants, while total-spin quantum numbers select entangled and non-Gaussian states from the same ground manifold. Adding density-density Hund interactions breaks the independent spin rotations and reduces the ground space to a spin-reversal pair with maximal magnetization. These states are extremely close to Slater determinants in their natural occupations, yet have finite two-body cumulants and conserved-operator algebras whose orbit dimensions differ substantially from the Slater values. Fe2O2 provides a larger example in which spatial mode entanglement can be substantial while fermionic non-Gaussianity remains weak, with the conserved-operator structure again distinguishing the state from the corresponding Slater transformation class. Together, these examples show that symmetry resolution, mode entanglement, reduced-density-matrix correlations, and conserved-operator structure provide complementary information about interacting and degenerate electronic ground states.
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BibTeX
@misc{petrovich2026symmetryresolved,
title = {{Symmetry-resolved fermionic correlations in iron-oxide ground spaces}},
author = {Federico Petrovich and Daniel Staros and Daniel N. Blaschke and Jian-Xin Zhu and M. Cerezo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36047},
eprint = {2610.36047},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36047},
}
RIS
TY - UNPB
TI - Symmetry-resolved fermionic correlations in iron-oxide ground spaces
AU - Federico Petrovich
AU - Daniel Staros
AU - Daniel N. Blaschke
AU - Jian-Xin Zhu
AU - M. Cerezo
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36047
UR - https://arxiv.org/abs/2610.36047
AB - Symmetries of quantum systems provide a natural way to organize the eigenspaces of many-body Hamiltonians. When degeneracies exist, however, they play a more subtle role as different sets of symmetry operators can resolve the same energy subspace into states with very different correlation properties. We study this interplay using a sequence of FeO and Fe_2O_2 models. For a Hubbard model of FeO, the ground space is 16-fold degenerate. Resolving it by local magnetizations gives a basis of Slater determinants, while total-spin quantum numbers select entangled and non-Gaussian states from the same ground manifold. Adding density-density Hund interactions breaks the independent spin rotations and reduces the ground space to a spin-reversal pair with maximal magnetization. These states are extremely close to Slater determinants in their natural occupations, yet have finite two-body cumulants and conserved-operator algebras whose orbit dimensions differ substantially from the Slater values. Fe_2O_2 provides a larger example in which spatial mode entanglement can be substantial while fermionic non-Gaussianity remains weak, with the conserved-operator structure again distinguishing the state from the corresponding Slater transformation class. Together, these examples show that symmetry resolution, mode entanglement, reduced-density-matrix correlations, and conserved-operator structure provide complementary information about interacting and degenerate electronic ground states.
ER -