Non-Hermiticity induced thermal entanglement phase transition

Theoretical analysis of a prototypical two-qubit effective non-Hermitian system characterized by asymmetric Heisenberg $XY$ interactions in the absence of external magnetic fields demonstrates that maximal bipartite entanglement and quantum phase transitions can be induced exclusively through non-Hermiticity. At thermal equilibrium as $T\rightarrow 0$, the system attains maximal entanglement ${C}=1$ for values of the non-Hermiticity parameter greater than a critical value $\gamma>\gamma_c=J\sqrt{(1-\delta^2)}$, where $J$ denotes the exchange interaction and $\delta$ represents the anisotropy of the system; conversely, for $\gamma < \gamma_c$, entanglement is nonmaximal and given by ${C} = \sqrt{(1 - (\gamma/J)^2)}$. The entanglement undergoes a discontinuous transition to zero precisely at $\gamma = \gamma_c$. This phase transition originates from the closing of the energy gap at a non-Hermiticity-driven ground state degeneracy, which is fundamentally different from an exceptional point. This work suggests the use of singular-value-decomposition generalized density matrix for the computation of entanglement in bi-orthogonal systems.