Scaling at chiral quantum critical points in two dimensions

TL;DR

This study investigates how disorder affects electron localization in two-dimensional chiral symmetric lattices, revealing a critical exponent near 2/3 that varies with magnetic field presence, contrasting previous findings.

Contribution

The paper provides a numerical analysis of localization length divergence at chiral quantum critical points, showing magnetic fields alter critical exponents within the chiral unitary class.

Findings

Critical exponent ound close to 2/3

Magnetic field influences the divergence behavior

Deviation from previously reported or zero magnetic field

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 \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.