Schwinger and Thirring models at finite chemical potential and temperature

The imaginary time generating functional Z for the massless Schwinger model at nonzero chemical potential mu and temperature T is studied in a torus with spatial length L. The lack of Hermiticity of the Dirac operator gives rise to a nontrivial mu- and T-dependent phase J in the effective action. When the Dirac operator has no zero modes (trivial sector), we evaluate J, which is a topological contribution, and we find exactly Z, the thermodynamical partition function, the boson propagator and the thermally averaged Polyakov loop. The mu-dependent contribution of the free partition function cancels exactly the nonperturbative one from J, for L-->infinity, yielding a zero charge density for the system, which bosonizes at nonzero mu. The boson mass is e/root pi, independent of T and mu, which is also the inverse correlation length between two opposite charges. Both the boson propagator and the Polyakov loop acquire a new T- and mu-dependent term at L-->infinity. The imaginary time generating functional for the massless Thirring model at nonzero T and mu is obtained exactly in terms of the above solution of the Schwinger model in the trivial sector. For this model, the mu dependences of the thermodynamical partition function, the total fermion number density and the fermion two-point correlation function are obtained. The phase J displayed here leads to our new results and allows us to complement nontrivially previous studies on those models.