## SciPost Submission Page

# Integrable Matrix Product States from boundary integrability

### by Balázs Pozsgay, Lorenzo Piroli, Eric Vernier

#### - Published as SciPost Phys. 6, 062 (2019)

### Submission summary

As Contributors: | Balázs Pozsgay |

Arxiv Link: | https://arxiv.org/abs/1812.11094v4 |

Date accepted: | 2019-05-17 |

Date submitted: | 2019-05-14 |

Submitted by: | Pozsgay, Balázs |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Mathematical Physics |

Approach: | Theoretical |

### Abstract

We consider integrable Matrix Product States (MPS) in integrable spin chains and show that they correspond to "operator valued" solutions of the so-called twisted Boundary Yang-Baxter (or reflection) equation. We argue that the integrability condition is equivalent to a new linear intertwiner relation, which we call the "square root relation", because it involves half of the steps of the reflection equation. It is then shown that the square root relation leads to the full Boundary Yang-Baxter equations. We provide explicit solutions in a number of cases characterized by special symmetries. These correspond to the "symmetric pairs" $(SU(N),SO(N))$ and $(SO(N),SO(D)\otimes SO(N-D))$, where in each pair the first and second elements are the symmetry groups of the spin chain and the integrable state, respectively. These solutions can be considered as explicit representations of the corresponding twisted Yangians, that are new in a number of cases. Examples include certain concrete MPS relevant for the computation of one-point functions in defect AdS/CFT.

###### Current status:

### Ontology / Topics

See full Ontology or Topics database.### Author comments upon resubmission

### List of changes

-We corrected the typos.

-We replaced the tensor product notation with $\cdot$ at the places requested.

### Submission & Refereeing History

- Report 2 submitted on 2019-05-12 19:12 by
*Anonymous* - Report 1 submitted on 2019-05-02 18:54 by
*Anonymous*