Entanglement of eta-pairing state with off-diagonal long-range order

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.

4 pages, 4 eps figures

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• Quantum discord and classical correlations in the bond-charge Hubbard model: quantum phase transitions, ODLRO and violation of the monogamy property for discord
• Entanglement in an SU(n) Valence-Bond-Solid State
• Entanglement in extended Hubbard models and quantum phase transitions
• Entanglement and Density Matrix of a Block of Spins in AKLT Model
• Entanglement in Valence-Bond-Solid States
• Exact eigenstates of extended SU($N$) Hubbard models: Generalizations of $\eta$-pairing states with $N$-particle off-diagonal long-range order
• Entanglement as a quantum order parameter
• $\eta$-pairing in correlated fermion models with spin-orbit coupling
• Structure of quantum correlations in momentum space and off diagonal long range order in eta pairing and BCS states
• Block Spin Density Matrix of the Inhomogeneous AKLT Model
• Reduced density matrix and entanglement entropy of permutationally invariant quantum many-body systems
• Rethinking Renormalization for Quantum Phase Transitions
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