Steinberg Matthew, Prior Javier
QuTech, Delft University of Technology, Delft, The Netherlands.
Quantum and Computer Engineering Department, Delft University of Technology, Delft, The Netherlands.
Sci Rep. 2022 Jan 11;12(1):532. doi: 10.1038/s41598-021-04375-5.
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.
超不变张量网络（hyMERA）被引入，作为在反德西特/共形场论（AdS/CFT）对应关系模拟中结合完美张量网络（HaPPY）和多尺度纠缠重整化假设（MERA）成功经验的一种方式。尽管这类新的张量网络在模拟具有准周期边界的双曲体流形产生的共形场论方面显示出很大潜力，但许多问题仍未解决。在本手稿中，我们分析了在hyMERA中针对某个准周期临界自旋链优化张量所涉及的挑战，并与MERA中的标准方法进行比较。此外，我们展示了两组新的张量分解，它们具有与原始构造不同的性质，这意味着多张量约束既不是唯一的，也不难找到，并且可能存在对迄今为止使用的解析张量形式的推广。最后，我们使用降阶超算子对几种研究的张量分解进行随机试验，发现hyMERA中对局部降阶超算子谱施加的约束与几个最小模型共形场论的算子谱兼容。
