Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2010-10-18
J. Stat. Mech. (2011) L03002
Physics
Condensed Matter
Strongly Correlated Electrons
10 pages, 4 figures, 1 table. Published version
Scientific paper
10.1088/1742-5468/2011/03/L03002
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.
Dubail Jerome
Stéphan Jean-Marie
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