State-resolved quantum-information fingerprints of partial dynamical symmetry in the interacting boson model
Abstract
Partial dynamical symmetry (PDS) is an algebraic structure in which a symmetry is neither exact nor fully broken: a subset of eigenstates keeps good quantum numbers and stays solvable while the rest mix. It is currently identified from spectroscopy. We ask whether it also leaves a purely structural mark in the eigenstates, and find, for the sd-IBM Hamiltonians studied here, that it does, though not in the magnitude of entanglement. The diagnostic is the variance of a symmetry Casimir, the label variance Var C[G], which shares its zero with a block-coherence entropy and a block impurity: all three vanish when a state occupies a single Casimir sector, a single irreducible representation once conjugate representations are resolved by the cubic Casimir. Resolved state by state, the variance is numerically zero on the symmetry-selected subset and large on the mixed states, isolating the PDS states from the wavefunctions alone; the separation does not close as the boson number grows and persists at Leviatan's first- and second-order critical points, whereas the magnitude of bipartite s|d entanglement does not separate the two families. We anchor the analysis in 168Er, reproducing Leviatan's fitted su3 admixtures and his Hamiltonian-parameter-independent γ → g B(E2) ratios. The diagnostic also has an exact dynamical form, a Casimir Loschmidt echo rigid on the symmetry-pure states, and we demonstrate its readout on an IBM superconducting processor at N=3, where a single solvable/mixed exemplar reproduces the predicted pattern within finite-shot uncertainties.
Related
- Ground-state entanglement and preserved dynamical symmetry in the interacting boson model
- Spectral symmetry fingerprints in equivariant representations
- Causal Fingerprints Reveal Hidden Mechanisms in Partially-Observed Dynamical Systems
- Spectral theory for dynamical large deviations in non-Markov self-interacting processes
- Symmetry-Reduced Variational Quantum Simulation of the U(5)→ SU(3) Quantum Phase Transition in the Interacting Boson Model
BibTeX
@misc{roy2026stateresolved,
title = {{State-resolved quantum-information fingerprints of partial dynamical symmetry in the interacting boson model}},
author = {Dhritimalya Roy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.04486},
eprint = {2608.04486},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.04486},
}
RIS
TY - UNPB
TI - State-resolved quantum-information fingerprints of partial dynamical symmetry in the interacting boson model
AU - Dhritimalya Roy
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2608.04486
UR - https://arxiv.org/abs/2608.04486
AB - Partial dynamical symmetry (PDS) is an algebraic structure in which a symmetry is neither exact nor fully broken: a subset of eigenstates keeps good quantum numbers and stays solvable while the rest mix. It is currently identified from spectroscopy. We ask whether it also leaves a purely structural mark in the eigenstates, and find, for the sd-IBM Hamiltonians studied here, that it does, though not in the magnitude of entanglement. The diagnostic is the variance of a symmetry Casimir, the label variance Var C[G], which shares its zero with a block-coherence entropy and a block impurity: all three vanish when a state occupies a single Casimir sector, a single irreducible representation once conjugate representations are resolved by the cubic Casimir. Resolved state by state, the variance is numerically zero on the symmetry-selected subset and large on the mixed states, isolating the PDS states from the wavefunctions alone; the separation does not close as the boson number grows and persists at Leviatan's first- and second-order critical points, whereas the magnitude of bipartite s|d entanglement does not separate the two families. We anchor the analysis in ^168Er, reproducing Leviatan's fitted su3 admixtures and his Hamiltonian-parameter-independent γ → g B(E2) ratios. The diagnostic also has an exact dynamical form, a Casimir Loschmidt echo rigid on the symmetry-pure states, and we demonstrate its readout on an IBM superconducting processor at N=3, where a single solvable/mixed exemplar reproduces the predicted pattern within finite-shot uncertainties.
ER -