# Non-Hermitian Chiral Magnetic Effect in Equilibrium

## TL;DR

This paper investigates the Chiral Magnetic Effect in non-Hermitian fermionic systems, revealing that it can occur in thermal equilibrium due to the lack of strict charge conservation, contrasting with Hermitian systems.

## Contribution

It demonstrates that non-Hermitian systems can exhibit the Chiral Magnetic Effect in equilibrium, challenging the traditional understanding based on Hermitian quantum mechanics.

## Key findings

- Chiral Magnetic Effect can occur in non-Hermitian systems at equilibrium.
- Charge conservation constraints differ in non-Hermitian systems.
- The Bloch theorem does not prevent currents in non-Hermitian thermodynamic systems.

## Abstract

We analyze the Chiral Magnetic Effect for non-Hermitian fermionic systems using the biorthogonal formulation of quantum mechanics. In contrast to the Hermitian chiral counterparts, we show that the Chiral Magnetic Effect may take place in thermal equilibrium of an open non-Hermitian system with, generally, massive fermions. The key observation is that for non-Hermitian charged systems, there is no strict charge conservation as understood in the Hermitian case, so the Bloch theorem preventing currents in the thermodynamic limit in equilibrium does not apply.