Logarithmic conformal field theory (LCFT) describes critical phenomena in non-Hermitian systems. In this work, we study a (1+1)D non-Hermitian massless free-fermion field theory and confirm its conformal invariance. We construct an infinite set of operators that satisfy the Virasoro algebra and identify the central charge 𝑐=−2. The spectrum of this model exhibits an indecomposable Jordan-cell structure, indicating that it is an LCFT. We further apply the same approach to critical lattice models and find that they display similar LCFT characteristics. Finally, we compute the indecomposability parameters 𝛽 at the first two levels and find that they coincide with those of the symplectic fermion theory, suggesting a close connection between the two theories.

Inviter: Xian-Xin Wu