Scaling at chiral quantum critical points in two dimensions

Abstract

We study the localization properties of electrons moving on two-dimensional bi-partite lattices in the presence of disorder. The models investigated exhibit a chiral symmetry and belong to the chiral orthogonal (chO), chiral symplectic (chS) or chiral unitary (chU) symmetry class. The disorder is introduced via real random hopping terms for chO and chS, while complex random phases generate the disorder in the chiral unitary model. In the latter case an additional spatially constant, perpendicular magnetic field is also applied. Using a transfer-matrix-method, we numerically calculate the smallest Lyapunov exponents that are related to the localization length of the electronic eigenstates. From a finite-size scaling analysis, the logarithmic divergence of the localization length at the quantum critical point at E=0 is obtained. We always find for the critical exponent κ, which governs the energy dependence of the divergence, a value close to 2/3. This result differs from the exponent κ=1/2 found previously for a chiral unitary model in the absence of a constant magnetic field. We argue that a strong constant magnetic field changes the exponent κwithin the chiral unitary symmetry class by effectively restoring particle-hole symmetry even though a magnetic field induced transition from the ballistic to the diffusive regime cannot be fully excluded.

arXiv comment7 pages, two figures

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Cited by in corpus (8)

• Critical delocalization of chiral zero energy modes in graphene
• Unifying the Anderson Transitions in Hermitian and Non-Hermitian Systems
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Metal-insulator transition in a 2D system of chiral unitary class
• Localization of Dirac modes in finite-temperature ${\mathbb{Z}}_2$ gauge theory on the lattice
• Generalized multifractality in 2D disordered systems of chiral symmetry classes
• Partial preservation of chiral symmetry and colossal magnetoresistance in adatom doped graphene
• Shape of the zeroth Landau level in graphene with non-diagonal disorder