光谱间隙的不可判定性（完整版）
Undecidability of the Spectral Gap (full version)
摘要：
我们表明，频谱间隙问题是不可判定的。具体来说，我们构建家庭的constitutionally-invariant，最近邻的哈密顿在一个二维正方形晶格的d-能级量子系统（d常数），其中确定系统是有间隙或无间隙是一个不可判定的问题。这是真的，即使每个哈密顿量是有隙或无隙的承诺在最强的意义上：它被承诺要么有连续谱以上的基态在热力学极限，或其光谱间隙是下界的热力学极限中的常数。此外，这个常数可以取为等于哈密顿量的局部相互作用强度。
英文摘要：
We show that the spectral gap problem is undecidable. Specifically, we construct families of translationally-invariant, nearest-neighbour Hamiltonians on a 2D square lattice of d-level quantum systems (d constant), for which determining whether the system is gapped or gapless is an undecidable problem. This is true even with the promise that each Hamiltonian is either gapped or gapless in the strongest sense: it is promised to either have continuous spectrum above the ground state in the thermodynamic limit, or its spectral gap is lower-bounded by a constant in the thermodynamic limit. Moreover, this constant can be taken equal to the local interaction strength of the Hamiltonian.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
