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arXiv quant-ph/0611264quant-phcond-mat.otherhep-th
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纠缠熵的统计依赖性

Statistics dependence of the entanglement entropy

M. Cramer, J. Eisert, M. B. Plenio

备注：
4 pages, 1 figure (essentially identical with published version)
发表信息：
Phys. Rev. Lett. 98, 220603 (2007)
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摘要：

量子多体系统的特殊区域的纠缠熵反映了其纯基态的纠缠。在这项工作中，我们建立这种纠缠临界准自由费米和玻色子晶格系统的标度律，而不诉诸数值手段。我们考虑D维半空间的几何设置，这使我们能够利用连接到一维的情况。有趣的是，我们发现了标度特性的差异，这取决于系统是否是玻色子-面积定律首次被证明成立-或费米，扩展了以前的立方区域的发现。对于具有近邻相互作用的玻色子系统，我们通过解析地计算对数负性证明了约束面积律。我们确定了一个长度尺度与纠缠，不同的相关长度。对于费米子，我们确定对数修正面积定律，这取决于费米表面的拓扑结构。我们发现Lifshitz量子相变伴随着首阶项的前因子的非解析性。

英文摘要：

The entanglement entropy of a distinguished region of a quantum many-body system reflects the entanglement present in its pure ground state. In this work, we establish scaling laws for this entanglement for critical quasi-free fermionic and bosonic lattice systems, without resorting to numerical means. We consider the geometrical setting of D-dimensional half-spaces which allows us to exploit a connection to the one-dimensional case. Intriguingly, we find a difference in the scaling properties depending on whether the system is bosonic - where an area-law is first proven to hold - or fermionic, extending previous findings for cubic regions. For bosonic systems with nearest neighbor interaction we prove the conjectured area-law by computing the logarithmic negativity analytically. We identify a length scale associated with entanglement, different from the correlation length. For fermions we determine the logarithmic correction to the area-law, which depends on the topology of the Fermi surface. We find that Lifshitz quantum phase transitions are accompanied with a non-analyticity in the prefactor of the leading order term.

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