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State-resolved quantum-information fingerprints of partial dynamical symmetry in the interacting boson model

Year: 2026
Type: preprint
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 $^{168}$Er, reproducing Leviatan's fitted $\su3$ admixtures and his Hamiltonian-parameter-independent $γ\!\to\! g$ $B(E2)$ 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.
DOI: 10.48550/arxiv.2608.04486
Open Access status: green
OpenAlex ID: W7197021172
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