Probing Band-center Anomaly with the Kernel Polynomial Method
arXiv:1910.09766 · doi:10.1088/1402-4896/abe322
Abstract
We investigate the anomalous behavior of localization length of a non-interacting one-dimensional Anderson model at zero temperature. We report numerical calculations of the Thouless expression of localization length, based on the Kernel polynomial method (KPM), which has an O(N ) computational complexity, where N is the system size. The KPM results show an excellent agreement with perturbative result in large system size limit, confirming the validity of Thouless formula. Thus, contrary to the previous numerical results, the KPM approximation of the Thouless expression produce the correct localization length at the band center. The Thouless expression relates localization length in terms of density of states in a one-dimensional disordered system. By calculating the KPM estimates of density of states, we find a cusp-like behavior around the band center in the perturbative regime. This cusp-like singularity can not be obtained by an approximate analytical calculations with in the second-order approximations, reflects the band-center anomaly.
arXiv comment17 pages, 4 figures
References in corpus (11)
- The Kernel Polynomial Method
- Localization and Mobility Edge in One-Dimensional Potentials with Correlated Disorder
- Anomalous Localization in Low-Dimensional Systems with Correlated Disorder
- Critical delocalization of chiral zero energy modes in graphene
- Band-center anomaly of the conductance distribution in one-dimensional Anderson localization
- Scaling and the center of band anomaly in a one-dimensional Anderson model with diagonal disorder
- Chebyshev-polynomial expansion of the localization length of Hermitian and non-Hermitian random chains
- Anomalous localisation near the band centre in the 1D Anderson model: Hamiltonian map approach
- Spectral Functions of One-Dimensional Systems with Correlated Disorder
- Anomalous localization enhancement in one-dimensional non-Hermitian disordered lattices
- The band-centre anomaly in the 1D Anderson model with correlated disorder