标题： 关于量子自旋链中无能隙基态上方谱隙的改进界 显示英文标题

标题： Improved bounds on the spectral gap above frustration free ground states of quantum spin chains

摘要： 在\cite{Nac2,Nac1}中，Nachtergaele 利用“鞅方法”得到了许多无阻挫量子自旋链的基态以上能隙的显式下界。我们对该主要结果进行了简单改进，从而可以得到自旋-1/2 铁磁 XXZ 链以上的能隙的一个精确下界。作为该方法的示例，我们还计算了 AKLT 模型的能隙的一个下界，约为预期值的 1/3。 显示英文摘要

摘要： In \cite{Nac2,Nac1} Nachtergaele obtained explicit lower bounds for the spectral gap above many frustration free quantum spin chains by using the ``martingale method''. We present simple improvements to his main bounds which allow one to obtain a sharp lower bound for the spectral gap above the spin-1/2 ferromagnetic XXZ chain. As an illustration of the method, we also calculate a lower bound for the spectral gap of the AKLT model, which is about 1/3 the size of the expected gap.