Thermal Activation of Divergent Distillable Entanglement under Non-Abelian Strong Symmetry
Heating usually destroys quantum entanglement. We show that thermalization constrained to a non-Abelian strong-symmetry sector can instead generate a distillable resource that diverges with system size. In an exactly solvable local dimer chain, entanglement across an equal bipartition is exactly zero at $T=0$, whereas every fixed $T>0$ yields $E_D=\frac12\log_2 N+C(T)+o(1)$. Measurements of the two half-chain representation labels convert thermally populated non-Abelian sectors into standard ebits. More generally, for global-singlet thermal states of finite-range, uniformly bounded, locally $SU(2)$-invariant chains, there is a nonzero high-temperature interval in which the protocol yield satisfies $Y_N=\frac12\log_2 N+O_\beta(1)$ and $E_D\geq Y_N$. For the dimer chain, the full finite-size onset is governed by a universal Bessel-function crossover with $T_*(N)=\Delta/[\ln N+O(1)]$. Exact diagonalization of a frustrated $J_1$-$J_2$ chain shows the expected finite-size signatures. Thus thermal fluctuations can create entanglement across a macroscopic cut and convert it into an unbounded operational quantum resource.