Conformal Properties of Hyperinvariant Tensor Networks

Abstract

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.

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• Entanglement distillation toward minimal bond cut surface in tensor networks
• Dual-isometric Projected Entangled Pair States
• Bulk-boundary correspondence from hyper-invariant tensor networks
• Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes
• Biased-Noise Thresholds of Zero-Rate Holographic Codes with Tensor-Network Decoding
• Absolutely maximally entangled pure states of multipartite quantum systems