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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 · Eric Vernier 
Arxiv Link:  https://arxiv.org/abs/1812.11094v4 (pdf) 
Date accepted:  20190517 
Date submitted:  20190514 02:00 
Submitted by:  Pozsgay, Balázs 
Submitted to:  SciPost Physics 
Academic field:  Physics 
Specialties: 

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 socalled twisted Boundary YangBaxter (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 YangBaxter 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 $(SO(N),SO(D)\otimes SO(ND))$, 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 onepoint functions in defect AdS/CFT.
Ontology / Topics
See full Ontology or Topics database.Published as SciPost Phys. 6, 062 (2019)
Author comments upon resubmission
List of changes
We corrected the typos.
We replaced the tensor product notation with $\cdot$ at the places requested.