Description of thermal entanglement with the static path plus random-phase approximation

Abstract

We discuss the application of the static path plus random phase approximation (SPA+RPA) and the ensuing mean field+RPA treatment to the evaluation of entanglement in composite quantum systems at finite temperature. These methods involve just local diagonalizations and the determination of the generalized collective vibrational frequencies. As illustration, we evaluate the pairwise entanglement in a fully connected XXZ chain of $n$ spins at finite temperature in a transverse magnetic field $b$. It is shown that already the mean field+RPA provides an accurate analytic description of the concurrence below the mean field critical region ($|b|<b_c$), exact for large $n$, whereas the full SPA+RPA is able to improve results for finite systems in the critical region. It is proved as well that for $T>0$ weak entanglement also arises when the ground state is separable ($|b|>b_c$), with the limit temperature for pairwise entanglement exhibiting quite distinct regimes for $|b|<b_c$ and $|b|>b_c$.

20 pages, 5 figures

References in corpus (4)

• A complete family of separability criteria
• Entanglement in a second order quantum phase transition
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Concurrence in collective models

Cited by in corpus (5)

• Entanglement of finite cyclic chains at factorizing fields
• Quantum phase transitions in fully connected spin models: an entanglement perspective
• Magnetic Properties and Thermal Entanglement on a Triangulated Kagome Lattice
• Evaluation of ground state entanglement in spin systems with the random phase approximation
• Evaluation of pairwise entanglement in translationally invariant systems with the random phase approximation