Extracting Boundary Conformal Data from Periodic Non-Hermitian Critical Chains

Abstract

Boundary conformal field theory (BCFT) contains universal data that are usually accessed microscopically by imposing spatial boundaries on the lattice. Here, we introduce a periodic-chain projected-partition-function spectroscopy that extracts universal boundary quantities directly from non-Hermitian bulk-critical quantum chains, avoiding the need to engineer microscopic open boundaries and circumventing subtle boundary effects in non-Hermitian systems. Using a short-range-entangled boundary preparation and its infrared-compatible left dual, we obtain the Affleck-Ludwig boundary entropy in non-Hermitian systems. We demonstrate this construction for two representative non-Hermitian infrared structures. For a $\mathcal{PT}$-symmetric Ising realization of the real nonunitary Yang-Lee CFT, we extract the minimal-boundary projected coefficient and recover a nontrivial negative excited-to-ground ratio. For the genuinely complex fixed points of the non-Hermitian five-state Potts chain, we resolve intrinsically complex boundary coefficients and reproduce the exact relation required by the Kramers-Wannier duality. Our results establish a route to nonunitary BCFT universal data via only knowledge of the bulk critical system, opening a window into non-Hermitian boundary criticality.