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.
Lorenzo Piroli, Pasquale Calabrese, Fabian H. L. Essler
SciPost Phys. 1, 001 (2016) ·
published 14 September 2016

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We study quantum quenches to the onedimensional Bose gas with attractive
interactions in the case when the initial state is an ideal onedimensional
Bose condensate. We focus on properties of the stationary state reached at late
times after the quench. This displays a finite density of multiparticle bound
states, whose rapidity distribution is determined exactly by means of the
quench action method. We discuss the relevance of the multiparticle bound
states for the physical properties of the system, computing in particular the
stationary value of the local pair correlation function $g_2$.
Dr Piroli: "To understand the approach to ..."
in Report on Quantum quenches to the attractive onedimensional Bose gas: exact results