非阿贝尔守恒定律产生的热激活长程纠缠
Thermal Activation of Divergent Distillable Entanglement under Non-Abelian Strong Symmetry
AI总结：
研究表明非阿贝尔守恒定律能将局部热涨落转化为操作资源，通过显式表示空间协议等方法，在有限高温区间使特定自旋链产生系统尺寸发散的可蒸馏纠缠，可精确求解的二聚体链有更明显效应，不可积链对角化结果与之相符。
AI中文摘要：
热噪声通常会抑制量子纠缠。我们表明，强非阿贝尔守恒定律可将局部热涨落转化为无界的操作资源。对于一类广泛的限制在全局单态扇区的有限范围SU(2)不变自旋链，一个显式表示空间协议在有限高温区间内产生\(Y_N=\frac{1}{2}\log_2N + O_\beta(1)\)，因此\(E_{\mathrm{D}}\geq Y_N\)。局部热涨落产生子系统自旋\(j\sim\sqrt{N}\)，其全局锁定的不可约表示包含\(\log_2(2j + 1)\sim\frac{1}{2}\log_2N\)个ebit。一个可精确求解的二聚体链表现出更明显的效应：其零温度状态在切割处无纠缠，而每个固定的\(T>0\)产生\(E_{\mathrm{D}}=\frac{1}{2}\log_2N + C(T) + o(1)\)，交叉尺度\(T_*(N)\sim\Delta/\ln N\)。一个不可积链的精确对角化与预测的标度一致。因此，当热化受非阿贝尔守恒定律限制时，加热可在宏观二分上激活系统尺寸发散的可蒸馏纠缠。
英文摘要：
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 $Y_N=\frac12\log_2 N+O_β(1)$ and $E_D\geq Y_N$. For the dimer chain, the full finite-size onset is governed by a universal Bessel-function crossover with $T_*(N)=Δ/[\ln N+O(1)]$. 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.
