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Entanglement compression in scale space: from the multiscale entanglement renormalization ansatz to matrix product operators (1912.10572v1)
Published 23 Dec 2019 in cond-mat.str-el, cond-mat.stat-mech, and hep-th
Abstract: The multiscale entanglement renormalization ansatz (MERA) provides a constructive algorithm for realizing wavefunctions that are inherently scale invariant. Unlike conformally invariant partition functions however, the finite bond dimension $\chi$ of the MERA provides a cut-off in the fields that can be realized. In this letter, we demonstrate that this cut-off is equivalent to the one obtained when approximating a thermal state of a critical Hamiltonian with a matrix product operator (MPO) of finite bond dimension $\chi$. This is achieved by constructing an explicit mapping between the isometries of a MERA and the local tensors of the MPO.