We analytically investigate the Liouvillian exceptional point manifolds (LEPMs) of a two-qubits open system, where one qubit is coupled to a dissipative polarization bath. Exploiting a $Z_2$ symmetry, we block diagonalize the Liouvillian and show that one symmetry block yields two planar LEPMs while the other one exhibits a more intricate, multisheet topology. The intersection curves of these manifolds provide a phase diagram for effective Zeno transitions at small dissipation. These results are consistent with a perturbative extrapolation from the strong Zeno regime. Interestingly, we find that the fastest relaxation to the nonequilibrium steady state occurs on LEPMs associated with the transition to the effective Zeno regime.

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• Nonequilibrium statistical mechanics
• Open quantum systems
• Quantum Zeno dynamics
• Quantum statistical mechanics
• Exceptional points
• Lindblad equation
• Spin chains