CORDIS
EU research results

CORDIS

English EN

Operator algebraic approach to topological phases

Objective

Topologically ordered phases are a new state of matter, discovered only around the late '80s. In recent years interest in such states has sparked, one of the reasons being applications to topological quantum computing: the topological properties make the state robust against perturbations, making them ideal components in an environment where (thermal or other) noise is one's biggest enemy. By now there is a plethora of examples of topologically ordered states, whose only unifying feature seems to be that they do not fall into the Landau theory of phases. Although there are many examples, the mathematical framework to rigorously study such systems is less clear, in particular if one wants to consider both so-called long range entangled phases and symmetry protected phases. The goal of this project is to tackle this problem.

The approach that is proposed is to use operator algebraic methods to focus on the algebraic properties of the observables in such systems. This approach has proved successful in algebraic quantum field theory. Using this attack the aim is to find tools to classify the different topological phases, and in particular find methods that are applicable a wide class of models, despite looking very different at first sight. These ideas will be tested on the wide range of topological systems that is available. The focus in this project is on stability properties on the one hand, in particular for invariants of topological phases, and the study of boundary theories on the other hand.
Leaflet | Map data © OpenStreetMap contributors, Credit: EC-GISCO, © EuroGeographics for the administrative boundaries

Coordinator

RHEINISCH-WESTFAELISCHE TECHNISCHE HOCHSCHULE AACHEN

Address

Templergraben 55
52062 Aachen

Germany

Activity type

Higher or Secondary Education Establishments

EU Contribution

€ 257 860,80

Partners (1)

Sort alphabetically

Expand all

THE REGENTS OF THE UNIVERSITY OF CALIFORNIA

Project information

Grant agreement ID: 657004

Status

Closed project

  • Start date

    1 September 2015

  • End date

    31 August 2018

Funded under:

H2020-EU.1.3.2.

  • Overall budget:

    € 257 860,80

  • EU contribution

    € 257 860,80

Coordinated by:

RHEINISCH-WESTFAELISCHE TECHNISCHE HOCHSCHULE AACHEN

Germany

This project is featured in...