128 research outputs found
Renyi entropy of highly entangled spin chains
Entanglement is one of the most intriguing features of quantum theory and a
main resource in quantum information science. Ground states of quantum
many-body systems with local interactions typically obey an "area law" meaning
the entanglement entropy proportional to the boundary length. It is exceptional
when the system is gapless, and the area law had been believed to be violated
by at most a logarithm for over two decades. Recent discovery of Motzkin and
Fredkin spin chain models is striking, since these models provide significant
violation of the entanglement beyond the belief, growing as a square root of
the volume in spite of local interactions. Although importance of intensive
study of the models is undoubted to reveal novel features of quantum
entanglement, it is still far from their complete understanding. In this
article, we first analytically compute the Renyi entropy of the Motzkin and
Fredkin models by careful treatment of asymptotic analysis. The Renyi entropy
is an important quantity, since the whole spectrum of an entangled subsystem is
reconstructed once the Renyi entropy is known as a function of its parameter.
We find non-analytic behavior of the Renyi entropy with respect to the
parameter, which is a novel phase transition never seen in any other spin chain
studied so far. Interestingly, similar behavior is seen in the Renyi entropy of
Rokhsar-Kivelson states in two-dimensions.Comment: 14+22 pages, 8 figures; (v2) references added, (v3) version to be
published in International Journal of Modern Physics
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