Non-Hermitian Chiral Magnetic Effect in Equilibrium

Maxim N Chernodub,Alberto Cortijo

doi:10.3390/sym12050761

Abstract

We analyze the chiral magnetic effect for non-Hermitian fermionic systems using the bi-orthogonal formulation of quantum mechanics. In contrast to the Hermitian counterparts, we show that the chiral magnetic effect takes place in equilibrium when a non-Hermitian system is considered. The key observation is that for non-Hermitian charged systems, there is no strict charge conservation as understood in Hermitian systems, so the Bloch theorem preventing currents in the thermodynamic limit and in equilibrium does not apply.

Highlights

The Chiral Magnetic Effect (CME) is the generation of an electric current J in the presence of an external magnetic field B [1]: e2 μ5 B. (1) h Ji =The current (1) appears naturally in a particular set of physical systems characterized by a broken invariance under the spatial reflection P
We demonstrated that CME in equilibrium is possible when non-Hermitian systems are considered
The key ingredient is to realize that the CME is zero if charge conservation is imposed in the system

Summary

Introduction

The Chiral Magnetic Effect (CME) is the generation of an electric current J in the presence of an external magnetic field B [1]: e2. The CME stems from the axial anomaly, which leads to non-conservation of the chiral current in Weyl systems described by the. The current is zero because the difference in the energies of the right- and left-hand chiral fermions does not create the true chiral imbalance. Once the chiral gauge field appears, the definition of the physical electric current starts to differ from the naive covariant version (3) by an addition of an extra term coming from the so-called Bardeen polynomials. This term cancels out this energy difference precisely, and the physical (so-called “consistent”) version of the current vanishes in thermal equilibrium (6). Non-Hermitian, they display a unitary evolution, and it is possible to define a consistent thermodynamics for them [16]

The Model

Computation of CSE and CME with Biorthogonal Quantum Mechanics

Conclusions