Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1511.08090 · Annals of Physics

Anyons and matrix product operator algebras

N. Bultinck, M. Mariën, Dominic J. Williamson, M.B. Şahinoğlu, J. Haegeman, Frank Verstraete

Published Jan 17, 2017• 179 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2017.01.004

Related papers

A remark on matrix product operator algebras, anyons and subfactors

Yasuyuki Kawahigashi

arXiv:1907.12169•Letters in Mathematical Physics•Jan 23, 2020•14 citations

Matrix Product States and Disordered Anyon Phase

WORLD SCIENTIFIC eBooks•Apr 1, 2023•0 citations

Anyons and quantum groups

Alberto Lerda A, S. Sciuto

arXiv:hep-th/9301100•Nuclear Physics B•Jul 1, 1993•89 citations

Two-dimensional topological order and operator algebras

Yasuyuki Kawahigashi

We review recent interactions between mathematical theory of two-dimensional topological order and operator algebras, particularly the Jones theory of subfactors. The role of representation theory in terms of tensor categories is emphasized. Connections to two-dimensional conformal field theory are also presented. In particular, we discuss anyon condensation, gapped domain walls and matrix product operators in terms of operator algebras.

arXiv:2102.10953•International Journal of Modern Physics B•Mar 30, 2021•13 citations

Spectrum Generating q-Algebras for Anyons

A. I. Solomon, Joseph L. Birman

Springer eBooks•Jan 1, 1994•2 citations

Matrix-product operator dualities in integrable lattice models

Yuan Miao, Andras Molnar, Nick G. Jones

Matrix-product operators (MPOs) appear throughout the study of integrable lattice models, notably as the transfer matrices. They can also be used as transformations to construct dualities between such models, both invertible (including unitary) and non-invertible (including discrete gauging). We analyse how the local Yang--Baxter integrable structures are modified under such dualities. We see that the $\check{R}$-matrix, that appears in the baxterization approach to integrability, transforms in a simple manner. We further argue for a broad class of MPO dualities that the usual Yang--Baxter $R$-matrix should be extended. This extended $R$-matrix satisfies modified algebraic relations, including a modified Yang--Baxter algebra previously identified in the unitary case, that altogether give a local integrable structure underlying the commuting transfer matrices of the dual model. We illustrate these results with two case studies, analysing an invertible unitary MPO and a non-invertible MPO both applied to the canonical XXZ spin chain. The former is the cluster entangler, arising in the study of symmetry-protected topological phases, while the latter is the Kramers--Wannier duality. We show several results for MPOs with exact MPO inverses that are of independent interest.

cond-mat.stat-mechCross-listedarXiv:2602.17436•Journal of Physics A Mathematical and Theoretical•Feb 20, 2026•0 citations
Matrix-product operators (MPOs) appear throughout the study of integrable lattice models, notably as the transfer matrices. They can also be used as transformations to construct dualities between such models, both invertible (including unitary) and non-invertible (including discrete gauging). We analyse how the local Yang--Baxter integrable structures are modified under such dualities. We see that the Rˇ\check{R}Rˇ-matrix, that appears in the baxterization approach to integrability, transforms in a simple manner. We further argue for a broad class of MPO dualities that the usual Yang--Baxter RRR-matrix should be extended. This extended RRR-matrix satisfies modified algebraic relations, including a modified Yang--Baxter algebra previously identified in the unitary case, that altogether give a local integrable structure underlying the commuting transfer matrices of the dual model. We illustrate these results with two case studies, analysing an invertible unitary MPO and a non-invertible MPO both applied to the canonical XXZ spin chain. The former is the cluster entangler, arising in the study of symmetry-protected topological phases, while the latter is the Kramers--Wannier duality. We show several results for MPOs with exact MPO inverses that are of independent interest.