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OATP SIGNED

Operator algebraic approach to topological phases

Total Cost €

0

EC-Contrib. €

0

Partnership

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Project "OATP" data sheet

The following table provides information about the project.

Coordinator
RHEINISCH-WESTFAELISCHE TECHNISCHE HOCHSCHULE AACHEN 

Organization address
address: TEMPLERGRABEN 55
city: AACHEN
postcode: 52062
website: www.rwth-aachen.de

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Germany [DE]
 Project website https://pieter.naaijkens.nl/mariecurie/
 Total cost 257˙860 €
 EC max contribution 257˙860 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2014
 Funding Scheme MSCA-IF-GF
 Starting year 2015
 Duration (year-month-day) from 2015-09-01   to  2018-08-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    RHEINISCH-WESTFAELISCHE TECHNISCHE HOCHSCHULE AACHEN DE (AACHEN) coordinator 257˙860.00
2    THE REGENTS OF THE UNIVERSITY OF CALIFORNIA US (OAKLAND CA) partner 0.00

Map

 Project 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.

 Publications

year authors and title journal last update
List of publications.
2018 Kohtaro Kato, Pieter Naaijkens
An entropic invariant for 2D gapped quantum phases
published pages: , ISSN: , DOI:
Preprint 2019-04-16
2018 Cha, Matthew; Naaijkens, Pieter; Nachtergaele, Bruno
On the stability of charges in infinite quantum spin systems
published pages: 1-37, ISSN: , DOI:
Preprint 2019-04-16
2017 Leander Fiedler, Pieter Naaijkens, Tobias J. Osborne
Jones index, secret sharing and total quantum dimension
published pages: 23039, ISSN: 1367-2630, DOI: 10.1088/1367-2630/aa5c0c
New Journal of Physics 19 2019-06-13
2017 Pieter Naaijkens
Subfactors and quantum information theory
published pages: 20, ISSN: , DOI:
2018-07-11
2017 Matthew Cha, Pieter Naaijkens, Bruno Nachtergaele
The Complete Set of Infinite Volume Ground States for Kitaev’s Abelian Quantum Double Models
published pages: , ISSN: 0010-3616, DOI: 10.1007/s00220-017-2989-4
Communications in Mathematical Physics 2019-06-13

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