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Exotic singular objects, known as exceptional points, are ubiquitous innon-Hermitian physics. They might be spectral singularities in energy bandsthat produce anomalous effects and defectiveness. The quantum entanglement of ageneric non-Hermitian model with two different types of spectral exceptionalpoints (SEPs) is systematically investigated in this paper. We discovered arelationship between non-unitary conformal field theories and the$k$-linear-type SEPs, which is typically associated with$\mathcal{PT}$-symmetry or pesdo-Hermicity spontaneous breaking. The underlyingassociation between $k$-square-root-type SEPs, which arise concurrently withreal (imaginary) gap closing in the complex spectrum, mimickingfirst-order-phase-transition criticalities, and complex conformal fieldtheories (cCFTs) is addressed through the calculation of complex centralcharges. From the entanglement spectrum, zero-energy exceptional modes arefound to be distinct from normal zero modes or topological boundary modes.Finally, we include a brief discussion of analogous non-Hermitian quantum spinmodels and endeavor to establish an intuitive understanding of exceptionalpoints through the spin picture in various scenarios.

Exceptional entanglement in non-Hermitian fermionic models