Evaluation of pairwise entanglement in translationally invariant systems with the random phase approximation

Abstract

We discuss a general mean field plus random phase approximation (RPA) for describing composite systems at zero and finite temperature. We analyze in particular its implementation in finite systems invariant under translations, where for uniform mean fields it requires just the solution of simple local-type RPA equations. As test and application, we use the method for evaluating the entanglement between two spins in cyclic spin 1/2 chains with both long and short range anisotropic XY-type couplings in a uniform transverse magnetic field. The approach is shown to provide an accurate analytic description of the concurrence for strong fields, for any coupling range, pair separation or chain size, where it predicts an entanglement range which can be at most twice that of interaction. It also correctly predicts the existence of a separability field together with full entanglement range in its vicinity. The general accuracy of the approach improves as the range of the interaction increases.

6 pages, 2 figures

References in corpus (6)

• Matrix product states represent ground states faithfully
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Divergence of the entanglement range in low dimensional quantum systems
• Concurrence in collective models
• Entanglement of finite cyclic chains at factorizing fields
• Description of thermal entanglement with the static path plus random-phase approximation

Cited by in corpus (5)

• Evaluation of ground state entanglement in spin systems with the random phase approximation
• Even-odd entanglement in boson and spin systems
• Generalized mean field description of entanglement in dimerized spin systems
• Phase diagram study of a dimerized spin-S zig-zag ladder
• Entanglement and area laws in weakly correlated gaussian states