Density of states for the $\pi$-flux state with bipartite real random hopping only: A weak disorder approach

Abstract

Gade [R. Gade, Nucl. Phys. B \textbf{398}, 499 (1993)] has shown that the local density of states for a particle hopping on a two-dimensional bipartite lattice in the presence of weak disorder and in the absence of time-reversal symmetry(chiral unitary universality class) is anomalous in the vicinity of the band center $\epsilon =0$ whenever the disorder preserves the sublattice symmetry. More precisely, using a nonlinear-sigma-model that encodes the sublattice (chiral) symmetry and the absence of time-reversal symmetry she argues that the disorder average local density of states diverges as $|\epsilon {|}^{-1}\exp (-c|\ln \epsilon {|}^{\kappa })$ with $c$ some non-universal positive constant and $\kappa =1/2$ a universal exponent. Her analysis has been extended to the case when time-reversal symmetry is present (chiral orthogonal universality class) for which the same exponent $\kappa =1/2$ was predicted. Motrunich \textit{et al.} [O. Motrunich, K. Damle, and D. A. Huse, Phys. Rev. B \textbf{65}, 064206 (2001)] have argued that the exponent $\kappa =1/2$ does not apply to the typical density of states in the chiral orthogonal universality class. They predict that $\kappa =2/3$ instead. We confirm the analysis of Motrunich \textit{et al.} within a field theory for two flavors of Dirac fermions subjected to two types of weak uncorrelated random potentials: a purely imaginary vector potential and a complex valued mass potential. This model is believed to belong to the chiral orthogonal universality class. Our calculation relies in an essential way on the existence of infinitely many local composite operators with negative anomalous scaling dimensions.

30 pages, final version published in PRB

References in corpus (7)

• Particle-hole symmetric localization in two dimensions
• Multifractality of wavefunctions at the quantum Hall transition revisited
• The supersymmetric technique for random-matrix ensembles with zero eigenvalues
• Freezing transitions and the density of states of 2D random Dirac Hamiltonians
• Spectral and Transport Properties of Quantum Wires with Bond Disorder
• Singular Density of States of Disordered Dirac Fermions in the Chiral Models
• Comment on ``Density of States of Disordered Two-Dimensional Crystals with Half-Filled Band''

Cited by in corpus (57)

• Anderson Transitions
• Electron transport in disordered graphene
• Strong disorder RG approach of random systems
• Random Network Models and Quantum Phase Transitions in Two Dimensions
• Disorder and Electronic Transport in Graphene
• Topological tight-binding models from non-trivial square roots
• Landauer conductance and twisted boundary conditions for Dirac fermions in two space dimensions
• Criticality and entanglement in random quantum systems
• Bond disordered spin liquid and the honeycomb iridate H${}_3$LiIr${}_2$O${}_6$ $-$ abundant low energy density of states from random Majorana hopping
• Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR lineshape
• Universal sign-control of coupling in tight-binding lattices
• Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors
• Anderson localization and the topology of classifying spaces
• Boundary criticality at the Anderson transition between a metal and a quantum spin Hall insulator in two dimensions
• Density of states in graphene with vacancies: midgap power law and frozen multifractality
• Metal-insulator transition from combined disorder and interaction effects in Hubbard-like electronic lattice models with random hopping
• Robustness of topological corner modes against disorder and application to acoustic networks
• Magic-Angle Semimetals with Chiral Symmetry
• Density of states in a two-dimensional chiral metal with vacancies
• Interaction effects on 2D fermions with random hopping
• Chalker scaling, level repulsion, and conformal invariance in critically delocalized quantum matter: Disordered topological superconductors and artificial graphene
• Termination of typical wavefunction multifractal spectra at the Anderson metal-insulator transition: Field theory description using the functional renormalization group
• Disordered d-wave superconductors with interactions
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Enhancement of critical temperatures in disordered bipartite lattices
• Emergent moments and random singlet physics in a Majorana spin liquid
• Vacancy-induced low-energy states in undoped graphene
• Exponents of the localization length in the 2D Anderson model with off-diagonal disorder
• Spectrum-wide quantum criticality at the surface of class AIII topological phases: An "energy stack" of integer quantum Hall plateau transitions
• Global phase diagram of two-dimensional Dirac fermions in random potentials
• Quantum Hall plateau transition in the lowest Landau level of disordered graphene
• Dirac fermions in a power-law-correlated random vector potential
• High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin-orbit effects and p-wave superconductivity
• Anomalous dimensions of operators without derivatives in the non-linear sigma-model for disordered bipartite lattices
• Metal-insulator transition in a 2D system of chiral unitary class
• Griffiths phase in the thermal quantum Hall effect
• Random hopping fermions on bipartite lattices: Density of states, inverse participation ratios, and their correlations in a strong disorder regime
• Beyond universal behavior in the one-dimensional chain with random nearest neighbor hopping
• Metal-insulator transition in Hubbard-like models with random hopping
• Disordered free fermions and the Cardy Ostlund fixed line at low temperature
• Disordered two-dimensional electron systems with chiral symmetry
• Generalized multifractality in 2D disordered systems of chiral symmetry classes
• Crossover of conductance and local density of states in a single-channel disordered quantum wire
• Strong disorder renormalization group on fractal lattices: Heisenberg models and magnetoresistive effects in tight binding models
• Logarithmic scaling of Lyapunov exponents in disordered chiral two-dimensional lattices
• Scaling at chiral quantum critical points in two dimensions
• Strong disorder effects of a Dirac fermion with a random vector field
• Dynamics of a quantum particle in low-dimensional disordered systems with extended states
• High-gradient operators in perturbed Wess-Zumino-Witten field theories in two dimensions
• Conductance fluctuations in disordered superconductors with broken time-reversal symmetry near two dimensions
• Role of the impurity-potential range in disordered d-wave superconductors
• Band-center metal-insulator transition in bond-disordered graphene
• Entanglement Entropy of $(2+1)$D Quantum Critical Points with Quenched Disorder: Dimensional Reduction Approach
• Universality, exponents and anomaly cancellation in disordered Dirac fermions
• Theory of the Anderson transition in three-dimensional chiral symmetry classes: Connection to type-II superconductors
• Critical States of Fermions with ${\mathbb{Z}}_2$ Flux Disorder
• Modulated honeycomb lattices and their magnetic properties