Search for localized Wannier functions of topological band structures via compressed sensing

We investigate the interplay of band structure topology and localization properties of Wannier functions. To this end, we extend a recently proposed compressed sensing based paradigm for the search for maximally localized Wannier functions [Ozolins et al., Proc. Natl. Acad. Sci. USA 110, 18368 (2013...

Full description

Saved in:
Bibliographic Details
Published in:Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2014-09, Vol.90 (11), Article 115110
Main Authors: Budich, J. C., Eisert, J., Bergholtz, E. J., Diehl, S., Zoller, P.
Format: Article
Language:English
Subjects:
Band structure of solids
Compressed
Condensed matter
Detection
Mathematical analysis
Mathematical models
Searching
Superconductors
Topology
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We investigate the interplay of band structure topology and localization properties of Wannier functions. To this end, we extend a recently proposed compressed sensing based paradigm for the search for maximally localized Wannier functions [Ozolins et al., Proc. Natl. Acad. Sci. USA 110, 18368 (2013) (http://dx.doi.org/10.1073/pnas.1318679110)]. We develop a practical toolbox that enables the search for maximally localized Wannier functions which exactly obey the underlying physical symmetries of a translationally invariant quantum lattice system under investigation. Most saliently, this allows us to systematically identify the most localized representative of a topological equivalence class of band structures, i.e., the most localized set of Wannier functions that is adiabatically connected to a generic initial representative. We also elaborate on the compressed sensing scheme and find a particularly simple and efficient implementation in which each step of the iteration is an O(N log N) algorithm in the number of lattice sites N. We present benchmark results on one-dimensional topological superconductors demonstrating the power of these tools. Furthermore, we employ our method to address the open question of whether compact Wannier functions can exist for symmetry-protected topological states such as topological insulators in two dimensions. The existence of such functions would imply exact flat-band models with finite range hopping. Here, we find numerical evidence for the absence of such functions. We briefly discuss applications in dissipative-state preparation and in devising variational sets of states for tensor network methods.
ISSN:1098-0121
1550-235X
DOI:10.1103/PhysRevB.90.115110