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

TL;DR

This paper explores how entanglement entropy in a spin-boson model relates to decoherence and quantum phase transitions, providing exact results and potential experimental measurement methods.

Contribution

It offers exact analytical solutions linking entanglement entropy with decoherence and phase transitions in a dissipative two-level system, confirmed by numerical methods.

Findings

Entanglement entropy obeys universal scalings.

Exact analytical results for entanglement entropy in spin-boson model.

Potential measurement of entanglement entropy in charge qubits.

Abstract

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.