Localization in random fractal lattices
arXiv:1701.04274 · doi:10.1103/PhysRevB.95.104206
Abstract
We investigate the issue of eigenfunction localization in random fractal lattices embedded in two dimensional Euclidean space. In the system of our interest, there is no diagonal disorder -- the disorder arises from random connectivity of non-uniformly distributed lattice sites only. By adding or removing links between lattice sites, we change the spectral dimension of a lattice but keep the fractional Hausdorff dimension fixed. From the analysis of energy level statistics obtained via direct diagonalization of finite systems, we observe that eigenfunction localization strongly depends on the spectral dimension. Conversely, we show that localization properties of the system do not change significantly while we alter the Hausdorff dimension. In addition, for low spectral dimensions, we observe superlocalization resonances and a formation of an energy gap around the center of the spectrum.
version accepted for publication in PRB, (7 pages, 8 figures)
References in corpus (13)
- Many-Body Physics with Ultracold Gases
- Localization of interacting fermions at high temperature
- Direct observation of Anderson localization of matter-waves in a controlled disorder
- Anderson localization in Bose-Einstein condensates
- Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
- Anderson localization and Mott insulator phase in the time domain
- Quantum quenches and many-body localization in the thermodynamic limit
- Quantum simulation of disordered systems with cold atoms
- Unusual localisation effects in quantum percolation
- Tailoring Anderson localization by disorder correlations in 1D speckle potentials
- Patterned Rydberg excitation and ionisation with a spatial light modulator
- Quantum percolation in granular metals
- The extended states in disordered 1D systems in the presence of the generalized -mer correlations