SciPost Phys. 6, 062 (2019) ·
published 27 May 2019

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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.
Eric Vernier, Jesper Lykke Jacobsen, Hubert Saleur
SciPost Phys. 2, 004 (2017) ·
published 21 February 2017

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We revisit the phase diagram of spin1 $su(2)_k$ anyonic chains, originally
studied by Gils {\it et. al.} [Phys. Rev. B, {\bf 87} (23) (2013)]. These
chains possess several integrable points, which were overlooked (or only
briefly considered) so far.
Exploiting integrability through a combination of algebraic techniques and
exact Bethe ansatz results, we establish in particular the presence of new
first order phase transitions, a new critical point described by a $Z_k$
parafermionic CFT, and of even more phases than originally conjectured. Our
results leave room for yet more progress in the understanding of spin1 anyonic
chains.