Entanglement at the quantum phase transition in a harmonic lattice

Abstract

The entanglement properties of the phase transition in a two dimensional harmonic lattice, similar to the one observed in recent ion trap experiments, are discussed both, for finite number of particles and thermodynamical limit. We show that for the ground state at the critical value of the trapping potential two entanglement measures, the negativity between two neighbouring sites and the block entropy for blocks of size 1, 2 and 3, change abruptly. Entanglement thus indicates quantum phase transitions in general; not only in the finite dimensional case considered in [Phys. Rev. Lett. {\bf 93}, 250404 (2004)]. Finally, we consider the thermal state and compare its exact entanglement with a temperature entanglement witness introduced in [Phys. Rev. A {\bf 77} 062102 (2008)].

extended published version

References in corpus (6)

• Quantum Phase Transitions and Bipartite Entanglement
• Dynamics of the entanglement between two oscillators in the same environment
• Criticality in correlated quantum matter
• Deterministic entanglement of ions in thermal states of motion
• Thermal state entanglement in harmonic lattices
• Double wells, scalar fields and quantum phase transitions in ions traps

Cited by in corpus (4)

• Quantum thermodynamics from the nonequilibrium dynamics of open systems: energy, heat capacity and the third law
• Separation-dependent localization in a two-impurity spin-boson model
• Driving many distant atoms into high-fidelity steady state entanglement via Lyapunov control
• Entanglement signatures of phase transition in higher-derivative quantum field theories