Closed-form construction of exceptional points in a two-parametric PT-symmetric large-matrix model

Stable bound states living on a discrete one-dimensional N-point lattice are assumed generated by a certain two-parametric PT symmetric potential $V=V(A,B)$. At any $N$, the coordinates $A=A^{(EP)}$ and $B=B^{(EP)}$ of the Kato’s exceptional point (marking the phase-transition instant of the loss of stability) are defined, exactly, via roots of a certain elementary quartic polynomial.