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

TL;DR

This paper models a two-level quantum system with many-body interactions and demonstrates a quantum dynamical phase transition characterized by a divergence in oscillation period and a transition to a Quantum Zeno phase.

Contribution

It introduces a microscopic Hamiltonian model and analytically solves the excitation dynamics, revealing a phase transition driven by environmental interaction strength.

Findings

Identifies a critical interaction threshold for phase transition.

Shows oscillation period divergence at the transition point.

Describes a transition to a Quantum Zeno phase with strong environmental coupling.

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 $1/\tau_{\phi}=1/(2\tau_{\mathrm{SE}% })$. However, beyond a finite critical interaction with the environment, $1/\tau_{\mathrm{SE}}>2\omega_{0}$, the decoherence rate becomes $1/\tau_{\phi}\propto(\omega_{0}^{2})\tau_{\mathrm{SE}}$. The oscillation period diverges showing a \emph{quantum dynamical phase transition}to a Quantum Zeno phase.