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

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 σ-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.

• Publication year

  2006

• Venue

  Nuclear Physics

• Publication date

  2006-05-22

• Fields of study

  Physics

• Identifiers
  DOI 10.1016/j.nuclphysb.2006.05.022arXiv cond-mat/0605533
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Crossover of conductance and local density of states in a single-channel disordered quantum wire

  2004cited by this paper
• Random hopping fermions on bipartite lattices: density of states, inverse participation ratios, and their correlations in a strong disorder regime

  2003cited by this paper
• Density of states for the π-flux state with bipartite real random hopping only: A weak disorder approach

  2002cited by this paper
• Erratum: Crossover from the chiral to the standard universality classes in the conductance of a quantum wire with random hopping only [Phys. Rev. B 62, 8249 (2000)]

  2001cited by this paper
• Particle-hole symmetric localization in two dimensions

  2001cited by this paper
• Multifractality and critical fluctuations at the Anderson transition

  2000cited by this paper
• Anderson localization in bipartite lattices

  2000cited by this paper
• gl(N|N) Super-current algebras for disordered Dirac fermions in two dimensions

  1999cited by this paper
• Topological transitions and freezing in XY models and Coulomb gases with quenched disorder: renormalization via traveling waves

  1999cited by this paper
• Random-mass Dirac fermions in doped spin-Peierls and spin-ladder systems: One-particle properties and boundary effects

  1997cited by this paper
• Delocalization transition via supersymmetry in one dimension

  1997cited by this paper
• Anderson localization for sublattice models

  1993cited by this paper
• The n = 0 replica limit of U(n) and U(n)SO(n) models☆

  1991cited by this paper
• Anomalous scaling laws in multifractal objects

  1987cited by this paper
• Inverse participation ratio in 2+ε dimensions

  1980cited by this paper
• Disordered system with n orbitals per site: n= [] limit

  1979cited by this paper
• Singular behavior of tight-binding chains with off-diagonal disorder

  1978cited by this paper
• Extended states in a one-demensional system with off-diagonal disorder

  1976cited by this paper
• Interaction of Goldstone Particles in Two-Dimensions. Applications to Ferromagnets and Massive Yang-Mills Fields

  1975cited by this paper

• Universality Classes of delocalization-localization transitions in Chiral Symplectic Class

  2025cites this paper
• Theory of Anderson transition in three-dimensional chiral symmetry classes: Connection to type-II superconductors

  2025cites this paper
• Generalized multifractality in two-dimensional disordered systems of chiral symmetry classes

  2023cites this paper
• Generalized multifractality at metal-insulator transitions and in metallic phases of two-dimensional disordered systems

  2022cites this paper
• Metal-insulator transition in a two-dimensional system of chiral unitary class

  2022cites this paper
• Spectrum-Wide Quantum Criticality at the Surface of Class AIII Topological Phases: An “Energy Stack” of Integer Quantum Hall Plateau Transitions

  2019cites this paper
• Metal-insulator transition from combined disorder and interaction effects in Hubbard-like electronic lattice models with random hopping

  2007cites this paper
• Anderson Transitions

  2007cites this paper
• The role of the impurity-potential range in disordered d-wave superconductors

  2006cites this paper
• Disordered d-wave superconductors with interactions

  2006cites this paper
• Disordered free fermions and the Cardy-Ostlund fixed line at low temperature

  2006cites this paper