Fermionic and bosonic partition functions at imaginary chemical potential as Bloch functions

TL;DR

This paper explores the phase transitions of certain quantum field models at finite temperature and imaginary chemical potential, revealing a mathematical mapping to lattice transformations and connections to Bloch functions, with implications for condensed matter physics.

Contribution

It introduces a novel mapping of phase transitions in quantum field models to lattice transformations and links partition functions to Bloch and Wannier functions, offering new analytical tools.

Findings

Phase transitions correspond to lattice transformations.

Zeros of Clausen functions inform phase behavior.

Partition functions relate to Bloch and Wannier functions.

Abstract

We point out that the phase transitions of the $d+1$ Gross-Neveu and $CP^{N-1}$ models at finite temperature and imaginary chemical potential can be mapped to transformations of Hubbard-like regular hexagonal to square lattice with the intermediate steps to be specific surfaces (irregular hexagonal kind) with an ordered construction based on the even indexed Bloch-Wigner-Ramakrishnan polylogarithm function. The zeros and extrema of the Clausen $Cl_d(\theta) $ function play an important role to the analysis since they allow us not only to study the fermionic and bosonic theories and their phase transitions but also the possibility to explore the existence of conductors arising from the correspondence between the partition functions of the two models and the Bloch and Wannier functions that play a crucial role in the tight-binding approximation in solid state physics.