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Non-Hermitian physics in open quantum many-body systems provides novelopportunities for the discovery of exotic quantum phenomena unexpected inHermitian systems. A previous study of the non-Hermitian Kondo problem inultracold atoms reports reversion of renormalization group flows which violatesthe $g$ theorem and produces an unusual quantum phase transition. In this work,we study the effect of electron-electron interactions by considering thenon-Hermitian Kondo problem in a Luttinger liquid. By performing a perturbativerenormalization group analysis to two-loop order, we find that the interplaybetween non-Hermitian Kondo couplings and electron-electron interactions canproduce a pair of complex fixed points. Complex fixed points have often beendiscussed in an attempt to understand the extremely long correlation length ofHermitian systems with weakly first-order transitions. Here, we show thatcomplex fixed points arise naturally and can be physically realized in openquantum systems. We discuss consequences of the complex fixed points and futuredirections.

Complex fixed points of the non-Hermitian Kondo model in a Luttinger liquid