Anomalous dimensions of operators without derivatives in the non-linear \(\sigma\)-model for disordered bipartite lattices
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Publication:879896
DOI10.1016/J.NUCLPHYSB.2006.05.022zbMATH Open1215.81075arXivcond-mat/0605533OpenAlexW2056012463MaRDI QIDQ879896
Publication date: 10 May 2007
Published in: Nuclear Physics B (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/cond-mat/0605533
Cites Work
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