Entanglement Entropy, decoherence, and quantum phase transition of a dissipative two-level system

Details Entanglement Entropy, decoherence, and quantum phase transition of a dissipative two-level system Entanglement Entropy, decoherence, and quantum phase transition of a dissipative two-level system

2007-11-14

arxiv.org/abs/0711.2301v3

Annals of Physics 323, 2208-2240 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

38 pages, 8 figures, related to cond-mat/0612095 and arXiv:0705.0957; final version to appear in Annals of Physics

Scientific paper

The concept of entanglement entropy appears in multiple contexts, from black hole physics to quantum information theory, where it measures the entanglement of quantum states. We investigate the entanglement entropy in a simple model, the spin-boson model, which describes a qubit (two-level system) interacting with a collection of harmonic oscillators that models the environment responsible for decoherence and dissipation. The entanglement entropy allows to make a precise unification between entanglement of the spin with its environment, decoherence, and quantum phase transitions. We derive exact analytical results which are confirmed by Numerical Renormalization Group arguments both for an ohmic and a subohmic bosonic bath. Those demonstrate that the entanglement entropy obeys universal scalings. We make comparisons with entanglement properties in the quantum Ising model and in the Dicke model. We also emphasize the possibility of measuring this entanglement entropy using charge qubits subject to electromagnetic noise; such measurements would provide an empirical proof of the existence of entanglement entropy.

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