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Symmetry-protected entanglement renormalization

机译:对称保护的纠缠重归一化

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摘要

Entanglement renormalization is a real-space renormalization group (RG) transformation for quantum many-body systems. It generates the multiscale entanglement renormalization ansatz (MERA), a tensor network capable of efficiently describing a large class of many-body ground states, including those of systems at a quantum critical point or with topological order. The MERA has also been proposed to be a discrete realization of the holographic principle of string theory. Here we propose the use of symmetric tensors as a mechanism to build a symmetry-protected RG flow, and discuss two important applications of this construction. First, we argue that symmetry-protected entanglement renormalization produces the proper structure of RG fixed points, namely, a fixed-point for each symmetry-protected phase. Second, in the context of holography, we show that by using symmetric tensors, a global symmetry at the boundary becomes a local symmetry in the bulk, thus explicitly realizing in the MERA a characteristic feature of the AdS/CFT correspondence.
机译:纠缠重归一化是用于量子多体系统的实空间重归一化组(RG)变换。它生成多尺度纠缠重归一化ansatz(MERA),这是一种张量网络,能够高效地描述一大类多体基态,包括处于量子临界点或拓扑顺序的系统。还提出了MERA是弦理论的全息原理的离散实现。在这里,我们建议使用对称张量作为建立对称保护的RG流的机制,并讨论该构造的两个重要应用。首先,我们认为对称保护的纠缠重归一化产生了RG不动点的正确结构,即每个对称保护相的一个固定点。其次,在全息术的背景下,我们表明通过使用对称张量,边界处的全局对称性成为整体中的局部对称性,因此在MERA中明确实现了AdS / CFT对应关系的特征。

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