Fig. 2

Bifurcation of eigenvalues under correlated dissipation. Real and imaginary parts of the eigenvalues of the effective evolution operator \(W_{\textrm{eff}}\) as a function of correlation strength \(\xi\) for several values of the statistical angle \(\theta\). Parameters are set to \(J = 0.1\), \(\gamma = 1\), and \(kT/\hbar \omega = 1\). For small \(\theta\), the bifurcation occurs near \(\xi \approx 0.1\), consistent with the bosonic limit. As \(\theta\) increases, the onset of PT symmetry breaking is delayed, requiring stronger correlations to induce the transition. In the fermionic limit (\(\theta \rightarrow \pi\)), relaxation is suppressed due to Pauli blocking and the exceptional point disappears.