Selfconsistent theory of mobility edges in quasiperiodic chains
Abstract
We introduce a selfconsistent theory of mobility edges in nearestneighbor tightbinding chains with quasiperiodic potentials. Demarcating boundaries between localized and extended states in the space of system parameters and energy, mobility edges are quite typical in quasiperiodic systems which lack the energyindependent selfduality of the commonly studied AubryAndréHarper model. The potentials in such systems are strongly and infiniterange correlated, reflecting their deterministic nature and rendering the problem distinct from that of disordered systems. Importantly, the underlying theoretical framework introduced is model independent, thus allowing analytical extraction of mobility edge trajectories for arbitrary quasiperiodic systems. We exemplify the theory using two families of models and show the results to be in very good agreement with the exactly known mobility edges as well as numerical results obtained from exact diagonalization.
 Publication:

Physical Review B
 Pub Date:
 February 2021
 DOI:
 10.1103/PhysRevB.103.L060201
 arXiv:
 arXiv:2012.01450
 Bibcode:
 2021PhRvB.103f0201D
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Quantum Gases;
 Condensed Matter  Statistical Mechanics;
 Quantum Physics
 EPrint:
 5 pages, 3 figures + Supplementary Material (2 pages)