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Infinite matrix product states, Conformal Field Theory and the Haldane-Shastry model

We generalize the Matrix Product States method using the chiral vertex operators of Conformal Field Theory and apply it to study the ground states of the XXZ spin chain, the J1-J2 model and random Heisenberg models. We compute the overlap with the exact wave functions, spin-spin correlators and the Renyi entropy, showing that critical systems can be described by this method. For rotational invariant ansatzs we construct an inhomogenous extension of the Haldane-Shastry model with long range exchange interactions.