Description
Conformal field theory (CFT) provides a powerful framework for describing critical phenomena in quantum systems. Non-Hermitian (NH) quantum systems are governed by non-Hermitian Hamiltonians, and one of their most striking features is the emergence of exceptional points (EPs), where eigenvalues and eigenstates coalesce. This naturally raises the question: what happens when these two ingredients are combined? In particular, when a non-Hermitian system becomes critical, can it still be described by a CFT? If so, what kind of CFT emerges?
In this work, we study a (1+1)-dimensional non-Hermitian massless free-fermion field theory and establish its conformal invariance. We construct an infinite set of operators satisfying the Virasoro algebra and identify the central charge as (c=-2). The spectrum of this model exhibits an indecomposable Jordan-cell structure, indicating that the theory is a logarithmic conformal field theory (LCFT). We further apply the same approach to critical lattice models and find that they exhibit similar logarithmic CFT characteristics. Our results suggest that non-Hermitian critical systems associated with exceptional points can be described by logarithmic conformal field theories.