Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2012-04-03
Physics
Condensed Matter
Disordered Systems and Neural Networks
7 pages, two figures
Scientific paper
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 \kappa, which governs the energy dependence of the divergence, a value close to 2/3. This result differs from the exponent \kappa=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 \kappa within 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.
Markos Peter
Schweitzer Ludwig
No associations
LandOfFree
Scaling at chiral quantum critical points in two dimensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Scaling at chiral quantum critical points in two dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Scaling at chiral quantum critical points in two dimensions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-354662