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arXiv · 2606.16785

Extracting Boundary Conformal Data from Periodic Non-Hermitian Critical Chains

Yifan Liu·Haruki Shimizu·Dongchang Liu·Kohei Kawabata
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Abstract

Boundary conformal field theory (BCFT) contains universal data that are usually accessed microscopically by imposing spatial boundaries on the lattice. In non-Hermitian many-body systems, however, changing boundary conditions can qualitatively reorganize spectra and eigenstates, and their boundary criticality remains elusive. Here, we introduce a periodic-chain spectroscopy to extract universal boundary quantities, such as the Affleck-Ludwig $g$-factor, 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. We illustrate our method with a $\mathcal{PT}$-symmetric Ising realization of the real nonunitary Yang-Lee CFT and reveal a universal negative excited-to-ground ratio, which has no counterpart in unitary critical theories and provides a microscopic signature of nonunitarity. For the genuinely complex fixed points of the non-Hermitian five-state Potts chain, we extract intrinsically complex boundary coefficients, verify the exact Kramers-Wannier duality relation, and select the consistent analytic-continuation branch of the boundary states. Our results establish a route to nonunitary BCFT universal data using only knowledge of the bulk critical system, opening a window into non-Hermitian boundary criticality.

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Yifan Liu, Haruki Shimizu, Dongchang Liu, Kohei Kawabata. 2026-06-15. Extracting Boundary Conformal Data from Periodic Non-Hermitian Critical Chains. https://arxiv.org/abs/2606.16785

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