Thermally Activated Long-Range Entanglement from Non-Abelian Conservation Laws

• URL: http://arxiv.org/abs/2607.12710v1
• Date: Tue, 14 Jul 2026 12:35:29 GMT
• Title: Thermally Activated Long-Range Entanglement from Non-Abelian Conservation Laws
• Abstract summary: We show that a strong non-Abelian conservation law can convert local thermal fluctuations into an unbounded operational resource.<n>Heat can activate system-size-diverging distillable entanglement across a macroscopic bipartition when thermalization is confined by a non-Abelian conservation law.
• Score: 1.599072005190786
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Thermal noise ordinarily suppresses quantum entanglement. We show that a strong non-Abelian conservation law can convert local thermal fluctuations into an unbounded operational resource. For a broad class of finite-range $SU(2)$-invariant spin chains restricted to the global-singlet sector, an explicit representation-space protocol yields $Y_N=\frac12\log_2 N+O_β(1)$, and hence $E_{\mathrm{D}}\geq Y_N$, throughout a finite high-temperature interval. Local thermal fluctuations produce subsystem spins $j\sim\sqrt N$, whose globally locked irreducible representations contain $\log_2(2j+1)\sim\frac12\log_2N$ ebits. An exactly solvable dimer chain exhibits a sharper effect: its zero-temperature state is unentangled across the cut, whereas every fixed $T>0$ produces $E_{\mathrm{D}}=\frac{1}{2}\log_2 N+C(T)+o(1)$, with crossover scale $T_*(N)\simΔ/\ln N$. Exact diagonalization of a nonintegrable chain is consistent with the predicted scaling. Thus heating can activate system-size-diverging distillable entanglement across a macroscopic bipartition when thermalization is confined by a non-Abelian conservation law.

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