Misc,
Entanglement of eta-pairing state with off-diagonal long-range order
(May 2004)
Abstract
Off-diagonal long-range order (ODLRO) is a quantum phenomenon not describable
in classical mechanical terms. It is believed to be one characteristic of
superconductivity. The quantum state constructed by eta-pairing which
demonstrates ODLRO is an eigenstate of the three-dimensional Hubbard model.
Entanglement is a key concept of the quantum information processing and has no
classical counterpart. We study the entanglement property of eta-pairing
quantum state. The concurrence is a well-known measure of quantum entanglement.
We show that the concurrence of entanglement between one-site and the rest
sites is exactly the correlation function of the ODLRO for the eta-pairing
state in the thermodynamic limit. So, when the eta-pairing state is entangled,
it demonstrates ODLRO and is thus in superconducting phase, if it is a
separable state, there is no ODLRO. In the thermodynamic limit, the
entanglement between M-site and other sites of the eta-pairing state does not
vanish. Other types of ODLRO of eta-pairing state are presented. We show that
the behavior of the ODLRO correlation functions is equivalent to that of the
entanglement of the eta-pairing state. The scaling of the entropy of the
entanglement for the eta-pairing state is studied.
