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 $ω_{0}$. For weak interactions with the environment $1/τ_{\mathrm{SE}}<2ω_{0},$ 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, $1/τ_{\mathrm{SE}}>2ω_{0}$, the decoherence rate becomes $1/τ_ϕ\propto(ω_{0}^{2})τ_{\mathrm{SE}}$. The oscillation period diverges showing a \emph{quantum dynamical phase transition}to a Quantum Zeno phase.