在平凡相中计算局部性质

摘要：

如果一个带空位的局部哈密顿量可以通过一条光滑的带空位的局部哈密顿量的路径与一个完全解耦的哈密顿量相连接，那么这个带空位的局部哈密顿量就是平凡相。对于这样的哈密顿量的基态，我们表明，当地的可观察的期望值可以计算在时间$\text{poly}(1/δ)$在一个空间维度和$e^{\text{poly}\log(1/δ)}$在两个和更高的维度，其中$δ$是所需的（添加剂）的准确性。该算法适用于系统的有限大小和在热力学极限。它只是假设存在，而不是任何道路的知识。

英文摘要：

A translation-invariant gapped local Hamiltonian is in the trivial phase if it can be connected to a completely decoupled Hamiltonian with a smooth path of translation-invariant gapped local Hamiltonians. For the ground state of such a Hamiltonian, we show that the expectation value of a local observable can be computed in time $\text{poly}(1/δ)$ in one spatial dimension and $e^{\text{poly}\log(1/δ)}$ in two and higher dimensions, where $δ$ is the desired (additive) accuracy. The algorithm applies to systems of finite size and in the thermodynamic limit. It only assumes the existence but not any knowledge of the path.

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。