AI 中文总结
研究李 - 杨哈密顿量，利用配分函数无零性证明在均匀\(Z\)场下基态有至少\(h/4\)能隙，且与系统大小和耦合强度无关，还给出计算其基态能量的多项式时间量子算法。
AI 中文摘要
李 - 杨定理及其量子扩展表明，对于任意图上的一大类哈密顿量，复磁场平面中配分函数的零点仅位于虚轴上。我们证明，对于这些哈密顿量，在任意强度\(h\)的均匀\(Z\)场下，基态具有至少\(h/4\)的能隙，与系统大小和耦合强度无关。证明利用了浅野以及铃木 - 费舍尔给出的配分函数的无零性，以表明任意\(Z\)算符乘积的虚时关联具有指数衰减。我们的结果给出了一种用于计算任意李 - 杨哈密顿量基态能量的多项式时间量子算法。
英文摘要
The Lee-Yang theorem and its quantum extensions state that, for a broad class of Hamiltonians on any graph, the partition function's zeros in the complex magnetic field plane lie only on the imaginary axis. For these Hamiltonians, we prove that under a uniform Z-field of any strength h, the ground state has a spectral gap of at least h/4, independent of the system size and of the coupling strengths. The proof uses the zero-freeness of the partition function as given by Asano and Suzuki-Fisher to show exponential decay of the imaginary-time correlations for any product of Z-operators. Our result gives a polynomial-time quantum algorithm for computing the ground state energy of any Lee-Yang Hamiltonian.
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