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We propose a multi-boundary generalization of thermofield double states (TFD)of a two-dimensional conformal field theory (CFT) and show, through a conformalmap to the complex plane, that they are closely related to multi-pointcorrelation functions. We then also describe how to approximately realize thesemulti-boundary TFD states numerically on the lattice, starting from a criticalquantum spin chain Hamiltonian. In addition, finite size corrections on thelattice are seen to be significantly reduced by the use of \textit{smoothers}-- numerically optimized unitary transformations that locally re-arrange thequantum spin degrees of freedom. One merit of the spin chain realization isthat it allows us to probe the properties of the proposed multi-boundary TFDstates through numerical experiments, including the characterization of theirentanglement structure. As an illustration, we explicitly construct generalizedTFD states with three and four boundaries for the Ising CFT and computeentanglement quantities using novel free fermion techniques. We find ranges ofparameters where their multipartite entanglement is significant or negligible.

Multi-boundary generalization of thermofield double states and their realization in critical quantum spin chains