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Since the realization of quantum systems described by non-HermitianHamiltonians with parity-time (PT) symmetry, interest in non-Hermitian, quantummany-body models has steadily grown. Most studies to-date map to traditionalquantum spin models with a non-Hermiticity that arises from making the modelparameters complex or purely imaginary. Here, we present a new set of modelswith non-Hermiticity generated by splitting a Hermitian term into twoJordan-normal form parts, and the perturbations are confined to one or twosites. We present exact diagonalization results for the PT-threshold in suchmodels, and provide an analytical approach for understanding the numericalresults. Surprisingly, with non-Hermitian potentials confined to two or even asingle site, we find a robust PT threshold that seems insensitive to the sizeof the quantum spin chain. Our results provide a pathway to experimentallyfeasible non-Hermitian quantum spin chains where the confluence of many-bodyeffects and non-Hermiticity effects can be observed.

$\mathcal{PT}$-Symmetry breaking in quantum spin chains with exceptional non-Hermiticities