Nonlinear σ model approach for level correlations in chiral disordered systems

We study level correlations of disordered systems with chiral unitary symmetry (AIII symmetry). We use a random matrix model with a finite correlation length to derive a supersymmetric nonlinear σ model. The result is compared with existing results based on other models. Using the methods of Kravtsov and Mirlin (Pis’ma Zh. Fksp. Teor. Fiz. 60, 645 (1994) [Sov. Phys. JETP 60, 656 (1994)]) and Andreev and Altshuler [Phys. Rev. Lett. 75, 902 (1995)], we calculate the density of states and two-level correlation function. The result is expressed using the spectral determinant as in traditional nonchiral systems. We discuss the renormalization of the mean level spacing which is not present in the traditional systems.