Phase structure of two-dimensional QED at zero temperature with flavor-dependent chemical potentials and the role of multidimensional theta functions

TL;DR

This paper analyzes the phase structure of two-dimensional QED with multiple flavors and flavor-dependent chemical potentials, revealing complex phase coexistence and the role of multidimensional theta functions at zero temperature.

Contribution

It introduces a detailed analysis of phase coexistence in multi-flavor 2D QED using multidimensional theta functions, highlighting exponential growth in phase coexistence points.

Findings

Infinite phases at zero temperature separated by first-order transitions.

Multiple phase coexistence points depending on flavor number.

Conjecture of exponential growth in coexisting phases with flavor number.

Abstract

We consider QED on a two-dimensional Euclidean torus with $f$ flavors of massless fermions and flavor-dependent chemical potentials. The dependence of the partition function on the chemical potentials is reduced to a $(2f-2)$-dimensional theta function. At zero temperature, the system can exist in an infinite number of phases characterized by certain values of traceless number densities and separated by first-order phase transitions. Furthermore, there exist many points in the $(f-1)$-dimensional space of traceless chemical potentials where two or three phases can coexist for $f=3$ and two, three, four or six phases can coexist for $f=4$. We conjecture that the maximal number of coexisting phases grows exponentially with increasing $f$.