Many-particle entanglement in the gaped antiferromagnetic Lipkin model

Abstract

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 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 ͑␥ = ϱ͒ to a maximally entangled state ͑␥ =0͒. 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 ␥ = 0: While at ␥ = 0 the entanglement grows logarithmically with the system size with no upper bound, it saturates for ␥ 0 at a level only depending on ␥.

Quantum entanglement in theS=1∕2spin ladder with ring exchange

“…Many works [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] have been devoted to understanding the relationship between QPT and the entanglement in different systems. It has been observed that quantum phase transitions are signaled by critical behaviors of concurrence [20], a measure of entanglement for two-qubit system, in a number of spin models [5,6,7,8,9]. For example, it was reported that the first derivative of the concurrence diverges at the transition point in the one-dimensional transverse field Ising model [5], while the concurrence shows cusplike behavior around the critical point in some 2D and 3D spin models [7].…”

Force sensors with precision beyond the standard quantum limit

“…(8) the sign of the coupling strengths of the non-linear spin terms depend on the sign of the detunings δ α , thus one could achieve ferromagnetic interaction δ α > 0 or respectively anti-ferromagnetic interaction δ α < 0. It is important to note that following the same line as in [27,28] our effective Hamiltonian (8) in the anti-ferromagnetic regime possesses supersymmetric structure at the special point ∆ = χ x χ y where we define χ 2 α = 4g 2 α /(N|δ α |). Indeed, it is straightforward to show that at this point the Hamiltonian (8) takes the form…”

Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections

“…It has also been recently used in optical cavity quantum electrodynamics in its dissipative version 8,9 for studying the decoherence of a single spin coupled to a spin bath 10,11 or quench dynamics 12 . Note also that, in recent years, the entanglement properties of its ground state 13,14,15,16,17,18,19,20,21,22 as well as the finite-size behavior 23,24,25,26 have focused much attention on this model. An exact solution of this model has been derived 27,28,29 , but it requires the solution of Bethe-like equations, which is more costly in terms of computational effort than exact diagonalization.…”