Search: onr:"swepub:oai:DiVA.org:kau-83611" >
Matrix product oper...
Matrix product operator symmetries and intertwiners in string-nets with domain walls
-
- Lootens, Laurens (author)
- Ghent University, BEL
-
- Fuchs, Jürgen, 1957- (author)
- Karlstads universitet,Institutionen för ingenjörsvetenskap och fysik (from 2013)
-
- Haegeman, Jutho (author)
- Ghent University, BEL
-
show more...
-
- Schweigert, Christoph (author)
- University of Hamburg, DEU
-
- Verstraete, Frank (author)
- Ghent University, BEL
-
show less...
-
(creator_code:org_t)
- SCIPOST FOUNDATION, 2021
- 2021
- English.
-
In: SciPost Physics. - : SCIPOST FOUNDATION. - 2542-4653. ; 10:3
- Related links:
-
https://doi.org/10.2...
-
show more...
-
https://kau.diva-por... (primary) (Raw object)
-
https://urn.kb.se/re...
-
https://doi.org/10.2...
-
show less...
Abstract
Subject headings
Close
- We provide a description of virtual non-local matrix product operator (MPO) symmetries in projected entangled pair state (PEPS) representations of string-net models. Given such a PEPS representation, we show that the consistency conditions of its MPO symmetries amount to a set of six coupled equations that can be identified with the pentagon equations of a bimodule category. This allows us to classify all equivalent PEPS representations and build MPO intertwiners between them, synthesising and generalising the wide variety of tensor network representations of topological phases. Furthermore, we use this generalisation to build explicit PEPS realisations of domain walls between different topological phases as constructed by Kitaev and Kong [Commun. Math. Phys. 313 (2012) 351-373]. While the prevailing abstract categorical approach is sufficient to describe the structure of topological phases, explicit tensor network representations are required to simulate these systems on a computer, such as needed for calculating thresholds of quantum error-correcting codes based on string-nets with boundaries. Finally, we show that all these string-net PEPS representations can be understood as specific instances of Turaev-Viro state-sum models of topological field theory on three-manifolds with a physical boundary, thereby putting these tensor network constructions on a mathematically rigorous footing.
Subject headings
- NATURVETENSKAP -- Fysik (hsv//swe)
- NATURAL SCIENCES -- Physical Sciences (hsv//eng)
Keyword
- Physics
- Fysik
Publication and Content Type
- ref (subject category)
- art (subject category)
Find in a library
To the university's database