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arXiv · 2502.02001

Complex entanglement entropy for complex conformal field theory

Haruki Shimizu·Kohei Kawabata
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Abstract

Conformal field theory underlies critical ground states of quantum many-body systems. While conventional conformal field theory is associated with positive central charges, nonunitary conformal field theory with complex-valued central charges has recently been recognized as physically relevant. Here, we demonstrate that complex-valued entanglement entropy characterizes complex conformal field theory and critical phenomena of open quantum many-body systems. This is based on non-Hermitian reduced density matrices constructed from the combination of right and left ground states. Applying the density matrix renormalization group to non-Hermitian systems, we numerically calculate the complex entanglement entropy of the non-Hermitian five-state Potts model, thereby confirming the scaling behavior predicted by complex conformal field theory.

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Haruki Shimizu, Kohei Kawabata. 2025-02-04. Complex entanglement entropy for complex conformal field theory. https://doi.org/10.1103/n578-ljd5

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