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.

7 pages, two figures

References in corpus (5)

• Anderson Transitions
• Exponents of the localization length in the 2D Anderson model with off-diagonal disorder
• Disordered two-dimensional electron systems with chiral symmetry
• Logarithmic scaling of Lyapunov exponents in disordered chiral two-dimensional lattices
• Critical conductance of the chiral 2d random flux model

Cited by in corpus (1)

• Generalized multifractality in 2D disordered systems of chiral symmetry classes