Quantum dynamical phase transition in a system with many-body interactions

Abstract

We introduce a microscopic Hamiltonian model of a two level system with many-body interactions with an environment whose excitation dynamics is fully solved within the Keldysh formalism. If a particle starts in one of the states of the isolated system, the return probability oscillates with the Rabi frequency ${\omega }_0$. For weak interactions with the environment $1/{\tau }_{\mathrm{SE}}<2{\omega }_0,$ we find a slower oscillation whose amplitude decays with a decoherence rate $1/τ_ϕ=1/(2τ_{\mathrm{SE}% })$. However, beyond a finite critical interaction with the environment, $1/{\tau }_{\mathrm{SE}}>2{\omega }_0$, the decoherence rate becomes $1/{\tau }_{\varphi }\propto ({\omega }_0^2){\tau }_{\mathrm{SE}}$. The oscillation period diverges showing a \emph{quantum dynamical phase transition}to a Quantum Zeno phase.

5 pages, 3 figures, minor changes, fig.2 modified, added references