Entanglement versus energy in quantum spin models

We study entanglement properties of all eigenstates of the Heisenberg XXX model, and find that the entanglement and mixedness for a pair of nearest-neighbor qubits are completely determined by the corresponding eigenenergies. Specifically, the negativity of the eigenenergy implies pairwise entanglement. From the relation between entanglement and eigenenergy, we obtain finite-size behaviors of the entanglement. We also study entanglement and mixedness versus energy in the quantum Heisenberg XY model.  2004 Elsevier B.V. All rights reserved. PACS: 03.65.Ud; 75.10.Jm Quantum entanglement lies at the heart of quantum mechanics, and can be exploited to accomplish some physical tasks such as quantum teleportation [1]. In this sense, it can be regarded as a resource, just like energy. As pointed out by Osborne and Nielsen [2], the similarity between entanglement and energy turns out to be more than superficial. It is interesting to explore the relationship between these two resources, entanglement and energy. Recently, the study of entanglement properties in many-body systems have received much attention [3–19]. Specifically, for the ground state (zero temperature) of a ring of N qubits interacting via the antiferromagnetic isotropic Heisenberg Hamiltonian, E-mail address: [email protected] (X. Wang). 0375-9601/$ – see front matter  2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2004.11.040 a direct relation is established between the concurrence C [20] quantifying the two-qubit entanglement and the ground-state energy per site 0 [10,21,22]: (1) C0(N)= max [ 0,−E0(N)/N ]= max[0,− 0(N)], where C refers to the concurrence for two nearestneighbor qubits, and E0 is the ground-state energy. For a pair of qubits, the entanglement of formation can be obtained from the concurrence C (2) Eof = h ( 1 +√1−C2