We present a characterization of the many-body lattice wave functionsobtained from the conformal blocks (CBs) of the Ising conformal field theory(CFT). The formalism is interpreted as a matrix product state using continuousancillary degrees of freedom. We provide analytic and numerical evidence thatthe resulting states can be written as BCS states. We give a complete proofthat the translationally invariant 1D configurations have a BCS form and wefind suitable parent Hamiltonians. In particular, we prove that the groundstate of the finite-size critical Ising transverse field (ITF) Hamiltonian canbe obtained with this construction. Finally, we study 2D configurations usingan operator product expansion (OPE) approximation. We associate these states tothe weak pairing phase of the $p+ip$ superconductor via the scaling of thepairing function and the entanglement spectrum.
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机译：我们提出了从伊辛共形场理论（CFT）的共形块（CBs）获得的多体晶格波函数的表征。形式主义被解释为使用连续辅助自由度的矩阵乘积状态。我们提供分析和数值证据，证明可以将所得状态表示为BCS状态。我们提供了一个完整的证明，即平移不变的一维配置具有BCS形式，并找到了合适的父哈密顿量。特别是，我们证明了使用此结构可以获得有限大小的临界伊辛横向场（ITF）哈密顿量的基态。最后，我们使用算子乘积展开（OPE）近似值研究2D配置。通过配对函数和纠缠谱的缩放，我们将这些状态与$ p + ip $超导体的弱配对阶段联系起来。
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