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

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 particle numbers 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.