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arXiv 1010.3716cond-mat.str-elcond-mat.stat-mech
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量子临界下二分保真度的普适行为

Universal behavior of a bipartite fidelity at quantum criticality

Jérôme Dubail, Jean-Marie Stéphan

摘要:

我们引入量子系统$A\cup B$的(对数)二分保真度作为其基态波函数和基态波函数之间的(对数)重叠,如果两个互补子系统$A$和$B$之间的相互作用被关闭,将获得。我们认为,它通常应满足面积法在尺寸$d>1$。在一维量子临界点(QCP)的情况下,我们发现它有一个普适的标度形式$\sim \ln \ell$,其中$\ell$是较小子系统的典型尺度.前因子与中心荷$c$成比例,并取决于几何形状。我们还认为,这个量可以是有用的,以定位量子相变,允许一个可靠的确定的中心荷,并在一般情况下表现出各种性质,是类似的纠缠熵。像纠缠熵一样,它包含了二维共形QCP中的次级普适项。

英文摘要:

We introduce the (logarithmic) bipartite fidelity of a quantum system $A\cup B$ as the (logarithm of the) overlap between its ground-state wave function and the ground-state one would obtain if the interactions between two complementary subsystems $A$ and $B$ were switched off. We argue that it should typically satisfy an area law in dimension $d>1$. In the case of one-dimensional quantum critical points (QCP) we find that it admits a universal scaling form $\sim \ln \ell$, where $\ell$ is the typical size of the smaller subsystem. The prefactor is proportional to the central charge $c$ and depends on the geometry. We also argue that this quantity can be useful to locate quantum phase transitions, allows for a reliable determination of the central charge, and in general exhibits various properties that are similar to the entanglement entropy. Like the entanglement entropy, it contains subleading universal terms in the case of a 2D conformal QCP.

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