Schwinger and Thirring models at finite chemical potential and temperature

Abstract

The imaginary time generating functional (Formula presented) for the massless Schwinger model at nonzero chemical potential (Formula presented) and temperature (Formula presented) is studied in a torus with spatial length (Formula presented). The lack of Hermiticity of the Dirac operator gives rise to a nontrivial (Formula presented)- and (Formula presented)-dependent phase (Formula presented) in the effective action. When the Dirac operator has no zero modes (trivial sector), we evaluate (Formula presented), which is a topological contribution, and we find exactly (Formula presented), the thermodynamical partition function, the boson propagator and the thermally averaged Polyakov loop. The (Formula presented)-dependent contribution of the free partition function cancels exactly the nonperturbative one from (Formula presented), for (Formula presented), yielding a zero charge density for the system, which bosonizes at nonzero (Formula presented). The boson mass is (Formula presented), independent of (Formula presented) and (Formula presented), which is also the inverse correlation length between two opposite charges. Both the boson propagator and the Polyakov loop acquire a new (Formula presented)- and (Formula presented)-dependent term at (Formula presented). The imaginary time generating functional for the massless Thirring model at nonzero (Formula presented) and (Formula presented) is obtained exactly in terms of the above solution of the Schwinger model in the trivial sector. For this model, the (Formula presented) dependences of the thermodynamical partition function, the total fermion number density and the fermion two-point correlation function are obtained. The phase (Formula presented) displayed here leads to our new results and allows us to complement nontrivially previous studies on those models. © 1998 The American Physical Society.