Complex entanglement entropy for complex conformal field theory

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.

11 pages, 5 figures

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Cited by in corpus (3)

• Spiral renormalization group flow and universal entanglement spectrum of the non-Hermitian 5-state Potts model
• Lattice and PT symmetries in tensor-network renormalization group: Case study of a hard-square lattice gas model
• Asymptotic freedom, lost: Complex conformal field theory in the two-dimensional $O(N>2)$ nonlinear sigma model and its realization in Heisenberg spin chains