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Unusual Times: Scientist 3

    Cartoon depicting entanglement

    Me and tensor networks are entangled during COVID-19. COVID-19? Sounds like I can never go outside. I have been staying at home for half a year. Not really alone, I have tensor networks with me. OK, they are not alive, but they are fun. What are tensor networks? You should ask Sir Roger Penrose for a better answer if you get a chance. But it is not such an easy thing to do. So, let me explain a little bit. Tensor networks consist of multiple tensors, connected, that is why we call them networks. Those networks reveal the engaged structure of many-body systems. Here in our Center, a special type of network, a tree tensor network (TTN), is being used to reveal the entanglement (and perhaps the coherence) between electronic and vibrational motion.

    Tree tensor network. Each node represents a tensor. Each skeleton represents a product.

    An interesting feature of TTN is, no matter which branch we cut, it will fall into two parts. This is because it does not have loops in its structure, just like a “tree”—you never find a loop of twig, at least in nature.

    Whichever branch is cut, the tree falls into two parts.

    Staying at home is not always a bad thing. It makes it possible for me to think about tensor networks deeply and sketch some cartoons (me and my tensor networks).

    The thing that makes tree tensor networks useful is that they tell us directly about the entangled structure of our systems. On each bond (connection), one may find a set of singular values that measure the degree of entanglement between the bipartite systems created by cutting this bond. I cannot resist this feature of the theory, which makes it a particularly appealing method to simulate the dynamics of electron-vibrational dynamics. And during the simulations, we can obtain the information of entanglement directly.

    Entanglement and coherence are important resources for understanding and perhaps manipulating energy transport. They may enhance the efficiency. Entanglement and coherence are important to research, too. During this tough time, I am entangled with a coherent group of researchers, virtually but firmly.

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