FisMat2017 - Submission - View

Abstract's title: Long-range topological insulators and weakened bulk-boundary correspondence
Submitting author: Luca Lepori
Affiliation: Università dell'Aquila; INFN Laboratori Nazionali del Gran Sasso
Affiliation Address: Dipartimento di Scienze Fisiche e Chimiche, Universita` dell’Aquila, via Vetoio, I-67010 Coppito-L’Aquila, Italy INFN, Laboratori Nazionali del Gran Sasso, Via G. Acitelli, 22, I-67100 Assergi (AQ), Italy.
Country: Italy
Oral presentation/Poster (Author's request): Oral presentation
Other authors and affiliations:
Abstract

We investigate the appearance of new types of insulators and
superconductors in long-range fermionic quantum systems, not included
in the famous ”ten-fold way classification”. This conclusion is
obtained analyzing at first specific one-dimensional models, in
particular their phase diagrams and entanglement properties. The
purely long-range phases are signaled for instance by the violation of
the area-law for the Von Neumann entropy and by a corresponding
peculiar entanglement spectrum. Later on, their origin is investigated
from a more general point of view and in any dimension, showing it
related with some divergences occurring in the spectrum. A satisfying
characterization for the long-range phases can be achieved, at least
in one dimension, as well as the connected definition of a nontrivial
topology, resulting in the presence of massive edge modes. Our results
allows us to infer the weakening of the bulk-boundary correspondence,
due to the important correlations between bulk and edges, and
consequently to clarify the nature of the massive edge modes. The
stability of the long-range phases against finite-size effects, very
relevant in current experiments, and against local disorder is finally
discussed.