Anomalous dimensions of operators without derivatives in the non-linear sigma-model for disordered bipartite lattices

TL;DR

This paper uses the fermionic path-integral formalism and non-linear sigma-models to analyze the anomalous dimensions of operators in disordered bipartite lattices, confirming previous results on the density of states.

Contribution

It demonstrates the effectiveness of the fermionic path-integral approach in deriving scaling behaviors in disordered bipartite lattice models.

Findings

Low-energy density of states matches earlier two-sublattice models.

Proper scaling operators identified for deviations from symmetry.

Validates the fermionic path-integral method despite controversial aspects.

Abstract

We consider a generic time-reversal invariant model of fermions hopping randomly on a square lattice. By means of the conventional replica-trick within the fermionic path-integral formalism, the model is mapped onto a non-linear sigma-model with fields spanning the coset U(4N)/Sp(2N), N->0. We determine the proper scaling combinations of an infinite family of relevant operators which control deviations from perfect two-sublattice symmetry. This allows us to extract the low-energy behavior of the density of states, which agrees with earlier results obtained in particular two-sublattice models with Dirac-like single-particle dispersion. The agreement proves the efficacy of the conventional fermionic-path-integral approach to disordered systems, which, in spite of many controversial aspects, like the zero-replica limit, remains one of the more versatile theoretical tool to deal with disordered electrons.