Abstract
Bipartite and global entanglement are analyzed for the ground state of a system of spin- particles interacting via a collective spin-spin coupling described by the Lipkin-Meshkov-Glick Hamiltonian. Under certain conditions, which include the special case of supersymmetry, the ground state can be constructed analytically. In the case of antiferromagnetic coupling and for an even number of particles, the system has a finite energy gap and the ground state undergoes a smooth transition, as a function of the continuous anisotropy parameter , from a separable to a maximally entangled state . From the analytic expression for the ground state, the bipartite entanglement between two subsets of spins as well as the global entanglement are calculated. Despite the absence of a quantum phase transition a discontinuous change of the scaling of the bipartite entanglement with the number of spins in the subsystem is found at the isotropy point : While at the entanglement grows logarithmically with the system size with no upper bound, it saturates for at a level only depending on .
- Received 17 November 2004
DOI:https://doi.org/10.1103/PhysRevA.72.022326
©2005 American Physical Society