# Non-Hermitian Chiral Magnetic Effect in Equilibrium

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## Abstract

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## 1. Introduction

## 2. The Model

## 3. Computation of CSE and CME with Biorthogonal Quantum Mechanics

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. The Hellman–Feynman Theorem for Bi-Orthogonal Systems

## Appendix B. Thermal Equilibrium Condition in Quasi-Hermitian Systems

## References

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**Figure 1.**(Color online) (

**a**) Band structure of $\mathcal{H}$ at zero magnetic field, but finite chemical potential. Contrary to Hermitian systems, the presence of chemical potentials might modify the spectrum strongly. (

**b**) Landau level spectrum for the non-Hermitian model for finite chemical potential $\mu $. Finite values of $\mu $ shift the Lowest Landau Level (LLL) spectrum (red) not only upwards or downwards, but also laterally. It is the lateral shift that makes the nonvanishing contribution from the LLL to the Chiral Magnetic Effect (CME).

**Figure 2.**(Color online) CME as a function of $\mu /m$ for three values of $\delta ={m}_{5}/m$. The vanishing CME for the Hermitian case, $\delta =0$, is recovered.

**Figure 3.**(Color online) (

**a**) Regularized CSE as a function of $\mu $ for three values of $\delta ={m}_{5}/m$. We fix the mass parameter to be $m=0.3$. (

**b**) CSE as a function of $\mu $ for three values of m and fixed $\delta =0.6$.

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**MDPI and ACS Style**

Chernodub, M.N.; Cortijo, A.
Non-Hermitian Chiral Magnetic Effect in Equilibrium. *Symmetry* **2020**, *12*, 761.
https://doi.org/10.3390/sym12050761

**AMA Style**

Chernodub MN, Cortijo A.
Non-Hermitian Chiral Magnetic Effect in Equilibrium. *Symmetry*. 2020; 12(5):761.
https://doi.org/10.3390/sym12050761

**Chicago/Turabian Style**

Chernodub, Maxim N., and Alberto Cortijo.
2020. "Non-Hermitian Chiral Magnetic Effect in Equilibrium" *Symmetry* 12, no. 5: 761.
https://doi.org/10.3390/sym12050761