Conformal properties of hyperinvariant tensor networks Steinberg, Matthew Prior, Javier We thank Santiago Oviedo-Casado, Javier Molina-Vilaplana, Matthias Volk, Sukhbinder Singh, and Michael Kastoryano for insightful discussions, as well as Alexander Jahn, Jens Eisert and Glen Evenbly for their feedback on the manuscript. J.P. is grateful for financial support from Ministerio de Ciencia, Innovación y Universidades (SPAIN), including FEDER (Grant no. PGC2018-097328-B-100) together with Fundación Séneca (Murcia, Spain) (Project no. 19882/GERM/15). M.S. wrote the main manuscript text. J.P. supervised and reviewed the manuscript. Hyperinvariant tensor networks (hyMERA) were introduced as a way to combine the successes of perfect tensor networks (HaPPY) and the multiscale entanglement renormalization ansatz (MERA) in simulations of the AdS/CFT correspondence. Although this new class of tensor network shows much potential for simulating conformal field theories arising from hyperbolic bulk manifolds with quasiperiodic boundaries, many issues are unresolved. In this manuscript we analyze the challenges related to optimizing tensors in a hyMERA with respect to some quasiperiodic critical spin chain, and compare with standard approaches in MERA. Additionally, we show two new sets of tensor decompositions which exhibit different properties from the original construction, implying that the multitensor constraints are neither unique, nor difficult to find, and that a generalization of the analytical tensor forms used up until now may exist. Lastly, we perform randomized trials using a descending superoperator with several of the investigated tensor decompositions, and find that the constraints imposed on the spectra of local descending superoperators in hyMERA are compatible with the operator spectra of several minimial model CFTs. 2022-02-10T12:00:14Z 2022-02-10T12:00:14Z 2022-01-11 journal article Steinberg, M., Prior, J. Conformal properties of hyperinvariant tensor networks. Sci Rep 12, 532 (2022). [https://doi.org/10.1038/s41598-021-04375-5] http://hdl.handle.net/10481/72785 10.1038/s41598-021-04375-5 eng http://creativecommons.org/licenses/by/3.0/es/ open access Atribución 3.0 España Nature Research