Effective quantum Zeno dynamics in dissipative quantum systems

TL;DR

This paper demonstrates that in dissipative quantum systems with strong local dissipation, the dynamics simplify to an effective Lindblad equation, enabling efficient computation of steady states, with validation on spin chains.

Contribution

It introduces a method to derive an effective Lindblad dynamics in the Zeno limit for open quantum systems with partial dissipation, simplifying analysis and computation.

Findings

Effective dynamics governed by a renormalized Lindblad equation in the Zeno limit

Eigenstate populations follow classical Markov processes

Proposed an efficient method for steady state evaluation in strongly dissipative systems

Abstract

We investigate the time evolution of an open quantum system described by a Lindblad master equation with dissipation acting only on a part of the degrees of freedom ${\cal H}_0$ of the system, and targeting a unique dark state in ${\cal H}_0$. We show that, in the Zeno limit of large dissipation, the density matrix of the system traced over the dissipative subspace ${\cal H}_0$, evolves according to another Lindblad dynamics, with renormalized effective Hamiltonian and weak effective dissipation. This behavior is explicitly checked in the case of Heisenberg spin chains with one or both boundary spins strongly coupled to a magnetic reservoir. Moreover, the populations of the eigenstates of the renormalized effective Hamiltonian evolve in time according to a classical Markov dynamics. As a direct application of this result, we propose a computationally-efficient exact method to evaluate the nonequilibrium steady state of a general system in the limit of strong dissipation.