SciPost Phys. 8, 016 (2020) ·
published 3 February 2020

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We consider the finite volume mean values of current operators in integrable
spin chains with local interactions, and provide an alternative derivation of
the exact result found recently by the author and two collaborators. We use a
certain type of long range deformation of the local spin chains, which was
discovered and explored earlier in the context of the AdS/CFT correspondence.
This method is immediately applicable also to higher rank models: as a concrete
example we derive the current mean values in the SU(3)symmetric fundamental
model, solvable by the nested Bethe Ansatz. The exact results take the same
form as in the Heisenberg spin chains: they involve the oneparticle
eigenvalues of the conserved charges and the inverse of the Gaudin matrix.
SciPost Phys. 6, 063 (2019) ·
published 28 May 2019

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We derive contour integral formulas for the real space propagator of the
spin$\tfrac12$ XXZ chain. The exact results are valid in any finite volume
with periodic boundary conditions, and for any value of the anisotropy
parameter. The integrals are on fixed contours, that are independent of the
Bethe Ansatz solution of the model and the string hypothesis. The propagator is
obtained by two different methods. First we compute it through the spectral sum
of a deformed model, and as a byproduct we also compute the propagator of the
XXZ chain perturbed by a DzyaloshinskiiMoriya interaction term. As a second
way we also compute the propagator through a lattice path integral, which is
evaluated exactly utilizing the socalled $F$basis in the mirror (or quantum)
channel. The final expressions are similar to the Yudson representation of the
infinite volume propagator, with the volume entering as a parameter. As an
application of the propagator we compute the Loschmidt amplitude for the
quantum quench from a domain wall state.
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.
Submissions
Submissions for which this Contributor is identified as an author:
Dr Pozsgay: "We are thankful to the Referee..."
in Report on Generalized Gibbs Ensemble and stringcharge relations in nested Bethe Ansatz