Locality of information in tensor networks quantum states

A many-body quantum state, such as one defined on lattice, or at topological settings such as quantum spin-liquids , is usually described by a coordinates vector in a tensor-product Hilbert-Space – a space with dimension that scales exponentially with the system size . This description is redundant and extremely difficult to use. An alternative description would be by a tensor-network, which is a large network-setup of small tensors, one for each lattice-site , which provides a more geometric and efficient description of the entanglement structure of the state .

Yet, for 2D systems it is very hard to perform computation using the network , even if one seeks for observables on a single site! Further assumptions have to be made. In the talk , I will assume a 2D tensor network that approximates a ground-state for a gapped local Hamiltonians, defined on a 2D lattice.  I will explain what constraints are enforced under this assumption, and how we can exploit them to ease on our calculations of expectation values. I will also explain  the basics of tensor networks, which have become a vastly important tool in condensed-matter physics for understanding and analyzing ground-states of local Hamiltonians.