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Integrable Matrix Product States from boundary integrability
by Balázs Pozsgay, Lorenzo Piroli, Eric Vernier
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Balázs Pozsgay · Eric Vernier |
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| Preprint Link: | https://arxiv.org/abs/1812.11094v4 (pdf) |
| Date accepted: | 2019-05-17 |
| Date submitted: | 2019-05-14 02:00 |
| Submitted by: | Pozsgay, Balázs |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
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| 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.
Author comments upon resubmission
List of changes
-We corrected the typos.
-We replaced the tensor product notation with $\cdot$ at the places requested.
Published as SciPost Phys. 6, 062 (2019)