Multifractality in aperiodic quantum spin chains

Abstract

Recently has been investigated that the ground-state wavefunction of the one dimensional quantum spin-1/2 chain models is multifractal in general with nontrivial fractal dimension. We are studying this phenomena for the quantum Ising chain with aperiodic perturbation. By performing a block real-space renormalization approach, we obtain the ground-state wave function and we extract the generalized multifractal dimension and the multifractal spectrum. For a spin chain with negative wandering exponent the multifractal quantities have the same behavior with the unperturbed chain while for a spin chain with a vanishing wandering exponent are dependent on the coupling ratio. Finally, for a spin chain with positive wandering exponent, the multifractal quantities present a different non-linear behavior. arXiv:1910.05931v1 [cond-mat.dis-nn]

Flat-band-based multifractality in the all-band-flat diamond chain

“…The disorder, in fact, facilitates the hybridization of the large-scale degenerate network of compact localized eigenstates and we see weak localization that is on the cusp of delocalization. In this Letter, we show that when the ABF chain is subjected instead to a quasiperiodic Aubry-André (AA) disorder [33,34], the eigenstates are in fact extended but non-ergodic thus exhibiting multifractality, a delicate phenomenon that has attracted a wave of interest in recent times [35][36][37][38][39][40][41][42]. The familiar 1-D Aubry-André Harper (AAH) tightbinding model [35,43,44], which is endowed with selfduality [33,45] exhibits multifractality [29] only at the metal-insulator transition that occurs at a critical poten-tial strength.…”