Classification of matrix product states with a local (gauge) symmetry

Ilya Kull*, Andras Molnar, Erez Zohar, J. Ignacio Cirac

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Matrix Product States (MPS) are a particular type of one dimensional tensor network states, that have been applied to the study of numerous quantum many body problems. One of their key features is the possibility to describe and encode symmetries on the level of a single building block (tensor), and hence they provide a natural playground for the study of symmetric systems. In particular, recent works have proposed to use MPS (and higher dimensional tensor networks) for the study of systems with local symmetry that appear in the context of gauge theories. In this work we classify MPS which exhibit local invariance under arbitrary gauge groups. We study the respective tensors and their structure, revealing known constructions that follow known gauging procedures, as well as different, other types of possible gauge invariant states.

Original languageAmerican English
Pages (from-to)199-241
Number of pages43
JournalAnnals of Physics
StatePublished - Nov 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Inc.


  • Lattice gauge theory
  • Matrix product state
  • Tensor network state


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