Complex entanglement entropy for complex conformal field theory

2025/02/04 by Haruki Shimizu, Shimizu, Haruki, Kohei Kawabata +1 · 8 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2502.02001

openalex publication_date 2025/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Complex Conformal Manifolds
• Non-hermitian Density Matrices from Time-like Entanglement and Wormholes
• Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls
• Complex nonlinear sigma model
• Entanglement complexification transition driven by a single non-Hermitian impurity
• PT symmetry-enriched non-unitary criticality
• Entropy Measures for Transition Matrices in Random Systems
• Spiral renormalization group flow and universal entanglement spectrum of the non-Hermitian 5-state Potts model

Related

• Relating non-Hermitian and Hermitian quantum systems at criticality
• Conformal Field Theory Ground States as Critical Points of an Entropy Function
• Operator content of real-space entanglement spectra at conformal critical points
• Entanglement complexification transition driven by a single non-Hermitian impurity
• Entanglement Entropy at Large Central Charge