Complex entanglement entropy for complex conformal field theory

TL;DR

This paper introduces complex entanglement entropy as a new tool to characterize complex conformal field theories and critical phenomena in non-Hermitian quantum systems, supported by numerical evidence.

Contribution

It demonstrates that complex entanglement entropy can characterize complex conformal field theories and criticality in non-Hermitian quantum many-body systems, a novel approach in the field.

Findings

Complex entanglement entropy characterizes complex CFTs.

Numerical confirmation using non-Hermitian five-state Potts model.

Scaling behavior matches predictions of 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.