  We report on ground state phases of a doped one-dimensional Hubbard model,
which for large onsite interactions is governed by the $t$-$J$ Hamiltonian,
where the extant entanglement is immutable under perturbative or sudden changes
of system parameters, a phenomenon termed as adiabatic freezing. We observe
that in the metallic Luttinger liquid phase of the model bipartite entanglement
decays polynomially and is adiabatically frozen, in contrast to the variable,
exponential decay in the phase-separation and superconducting spin-gap phases.
Significantly, at low fixed electron densities, the spin-gap phase shows
remarkable affinity to doped resonating valence bond gas, with multipartite
entanglement frozen across all parameter space. We note that entanglement, in
general, is sensitive to external perturbation, as observed in several systems,
and hitherto, no such invariance or freezing behavior has been reported.
