Entanglement vs. gap for one-dimensional spin systems
Entanglement vs. gap for one-dimensional spin systems
复制标题
一维自旋系统的纠缠与间隙
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
D. Gottesman
中科院分区：
文献类型：
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作者：
M. Hastings;D. Aharonov;D. Gottesman
我们研究了一维局域哈密顿量的纠缠与谱隙的关系。一维系统的面积定律表明，对于基态，任何区间的纠缠都是一个与区间大小无关的常数的上界。然而，上界对谱隙{Delta}的可能依赖是未知的，因为最已知的一般上界在渐近上远大于先前为小的{Delta}构建的任何模型系统的最大可能的熵。为了解决这一渐近行为，我们构造了一族一维局域系统，其中某些区间的纠缠熵在1/{Delta}中是多项式的，而以前研究的系统的所有区间的纠缠熵都有一个常数倍的对数(1/{Delta})。
We study the relationship between entanglement and spectral gap for local Hamiltonians in one dimension. The area law for a one-dimensional system states that for the ground state, the entanglement of any interval is upper-bounded by a constant independent of the size of the interval. However, the possible dependence of the upper bound on the spectral gap {Delta} is not known, as the best known general upper bound is asymptotically much larger than the largest possible entropy of any model system previously constructed for small {Delta}. To help resolve this asymptotic behavior, we construct a family of one-dimensional local systems for which some intervals have entanglement entropy which is polynomial in 1/{Delta}, whereas previously studied systems had the entropy of all intervals bounded by a constant times log(1/{Delta}).