Bi-partite and global entanglement in a many-particle system with collective spin coupling
Loading...
Date
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
Bipartite and global entanglement are analyzed for the ground state of a system of $N$ spin 1/2 particles interacting via a collective spin-spin coupling described by the Lipkin-Meshkov-Glick (LMG) Hamiltonian. Under certain conditions which includes the special case of a super-symmetry, the ground state can be constructed analytically. In the case of an anti-ferromagnetic coupling and for an even number of particles this state undergoes a smooth crossover as a function of the continuous anisotropy parameter $γ$ from a separable ($γ=\infty $) to a maximally entangled many-particle state ($γ=0$). From the analytic expression for the ground state, bipartite and global entanglement are calculated. In the thermodynamic limit a discontinuous change of the scaling behavior of the bipartite entanglement is found at the isotropy point $γ=0$. For $% γ=0$ the entanglement grows logarithmically with the system size with no upper bound, for $γ\neq 0$ it saturates at a level only depending on $γ$. For finite systems with total spin $J=N/2$ the scaling behavior changes at $γ=γ_{\mathrm{crit}}=1/J$.
8 pages, 5 figures, submitted to Phys. Rev. A
8 pages, 5 figures, submitted to Phys. Rev. A