Ground state entanglement in one-dimensional translationally invariant quantum systems
Ground state entanglement in one-dimensional translationally invariant quantum systems
复制标题
一维平移不变量子系统中的基态纠缠
DOI：
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发表时间：
2009
期刊：
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通讯作者：
S. Irani
中科院分区：
文献类型：
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作者：
S. Irani
我们研究是否有可能为一维的非线性不变的哈密顿量具有基态与高度的纠缠。我们提出了一个家庭的conventionally不变的哈密顿量{Hn}的无限链。Hn的谱隙为Ω（1/poly（n））。此外，对于Hn和任意m的基空间中的任何状态，存在具有纠缠熵Ω（min{m，n}）的大小为m的区域。一个类似的结构产生的有限链，具有独特的基态表现出高纠缠的conventionally不变的哈密顿。Hastings证明的面积定律[“An area law for one dimensional quantum systems，”J. Stat.机械：理论实验2007（08024）]给出了一维基态纠缠熵的恒定上限，该上限与区域的大小无关，但指数地依赖于1/Δ，其中Δ是谱隙。本文给出了一个下界，给出了一类纠缠熵与1/Δ成多项式关系的哈密顿量。P...
We examine whether it is possible for one-dimensional translationally invariant Hamiltonians to have ground states with a high degree of entanglement. We present a family of translationally invariant Hamiltonians {Hn} for the infinite chain. The spectral gap of Hn is Ω(1/poly(n)). Moreover, for any state in the ground space of Hn and any m, there are regions of size m with entanglement entropy Ω(min{m,n}). A similar construction yields translationally invariant Hamiltonians for finite chains that have unique ground states exhibiting high entanglement. The area law proven by Hastings [“An area law for one dimensional quantum systems,” J. Stat. Mech.: Theory Exp. 2007 (08024)] gives a constant upper bound on the entanglement entropy for one-dimensional ground states that is independent of the size of the region but exponentially dependent on 1/Δ, where Δ is the spectral gap. This paper provides a lower bound, showing a family of Hamiltonians for which the entanglement entropy scales polynomially with 1/Δ. P...