Fermions coupled to Chern-Simons gauge field or imaginary chemical potential and the Bloch theorem

TL;DR

This paper explores the equivalence of certain 3D fermionic theories at finite temperature and imaginary chemical potential, revealing a connection to Bloch waves and their impact on vacuum structure and quasiparticle behavior.

Contribution

It demonstrates the equivalence between Chern-Simons fermion theory and the Gross-Neveu model at finite temperature with imaginary chemical potential, and links the vacuum structure to Bloch wave phenomena.

Findings

Thermodynamic results are identical in both models.

Vacuum structure exhibits Bloch wave characteristics.

Fermionic and bosonic quasiparticles depend on band position.

Abstract

I point out that the $U(N)$ Chern-Simons $3d$ theory coupled to fermions at finite temperature and at a specific mean field approximation and the $3d$ Gross-Neveu model at finite temperature and imaginary chemical potential can give us the same results for the thermodynamic values of the free-energy and the saddle point equation for the thermal mass. I further argue that the periodic structure of the imaginary chemical potential brings also Bloch's theorem into the game. Namely, the vacuum structure of the fermionic system with imaginary baryon density is a Bloch wave. I further emphasise that Bloch waves correspond to fermionic (antisymmetric) or bosonic (symmetric) quasi-particles depending on the point in the band one sits in.